STRAIGHT LINES - Pyqs

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The equation of the line passing through $(2,3)$ and making an angle $45^\circ$ with the positive $x$-axis is
(Exam: IIT-JEE Year: 1998)

(A) $y-3=x-2$

(B) $y-3=2(x-2)$

(D) $x+y=5$

The distance of the point $(1,2)$ from the line $3x+4y-10=0$ is
(Exam: AIPMT Year: 2002)

(A) $\frac{1}{5}$

(B) $\frac{3}{5}$

(D) $\frac{7}{5}$

The slope of the line $2x-5y+7=0$ is
(Exam: JEE Main Year: 2013)

(A) $\frac{5}{2}$

(B) $-\frac{2}{5}$

(D) $-\frac{5}{2}$

The equation of the line parallel to $3x-4y+5=0$ and passing through origin is
(Exam: BITSAT Year: 2006)

(A) $3x-4y=0$

(B) $4x+3y=0$

(D) $4x-3y=0$

The angle between the lines $y=x$ and $y=-x$ is
(Exam: IIT-JEE Year: 1995)

(A) $45^\circ$

(B) $60^\circ$

(D) $30^\circ$

The equation of the perpendicular bisector of the line joining $(1,2)$ and $(3,4)$ is
(Exam: NEET Year: 2018)

(A) $y=x$

(B) $x+y=5$

(D) $2x+y=7$

If the line $ax+by+1=0$ passes through $(1,1)$, then $a+b=$
(Exam: KVPY Year: 2010)

(A) $-1$

(B) $0$

(D) $2$

The intercepts made by the line $2x+3y=6$ on the coordinate axes are
(Exam: JEE Main Year: 2016)

(A) $3,2$

(B) $2,3$

(D) $3,3$

The line through $(1,-2)$ perpendicular to $3x+4y+5=0$ is
(Exam: AIIMS Year: 2009)

(A) $4x-3y+2=0$

(B) $3x+4y-5=0$

(D) $3x-4y+5=0$

Q10

The condition for the lines $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$ to be coincident is
(Exam: IIT-JEE Year: 1993)

(A) $\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}$

(B) $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

(D) $a_1b_2-a_2b_1=0$

Q11

The area of the triangle formed by the coordinate axes and the line $x+y=4$ is
(Exam: JEE Main Year: 2012)

(A) $4$

(B) $6$

(D) $16$

Q12

The equation of the line with slope $m$ and $y$-intercept $c$ is
(Exam: NEET Year: 2020)

(A) $y=mx+c$

(B) $y=mx-c$

(D) $mx+y+c=0$

Q13

The point of intersection of the lines $x+y=2$ and $x-y=0$ is
(Exam: BITSAT Year: 2008)

(A) $(1,1)$

(B) $(2,0)$

(D) $(1,0)$

Q14

If the slope of a line is zero, the line is
(Exam: JEE Main Year: 2014)

(A) vertical

(B) horizontal

(D) coincident with $y=x$

Q15

The slope of the line joining $(x_1,y_1)$ and $(x_2,y_2)$ is
(Exam: Olympiad Year: 2005)

(A) $\frac{x_2-x_1}{y_2-y_1}$

(B) $\frac{y_2-y_1}{x_2-x_1}$

(D) $\frac{y_1+y_2}{x_1+x_2}$

Q16

The line $x=3$ is
(Exam: JEE Main Year: 2019)

(A) horizontal

(B) vertical

(D) parallel to $y$-axis

Q17

The equation of the family of lines through $(1,1)$ is
(Exam: IIT-JEE Year: 1999)

(A) $y-1=m(x-1)$

(B) $y=mx+1$

(D) $mx+y=1$

Q18

The angle between the line $y=mx$ and the $x$-axis is
(Exam: NEET Year: 2017)

(A) $\tan^{-1}m$

(B) $\sin^{-1}m$

(D) $\tan m$

Q19

The condition for two lines to be perpendicular is
(Exam: JEE Main Year: 2011)

(A) $m_1=m_2$

(B) $m_1+m_2=0$

(D) $m_1m_2=1$

Q20

The equation of the line joining $(0,0)$ and $(a,b)$ is
(Exam: AIIMS Year: 2007)

(A) $bx-ay=0$

(B) $ax-by=0$

(D) $bx+ay=0$

Q21

The locus of a point whose distances from the lines $x=2$ and $y=3$ are equal is
(Exam: JEE Main Year: 2015)

(A) $x-y+1=0$

(B) $x+y-5=0$

(D) $x+y=5$

Q22

The equation of the line passing through the intersection of $x+y=1$ and $2x-y=3$ and perpendicular to $x-2y+4=0$ is
(Exam: IIT-JEE Year: 2001)

(A) $2x+y-5=0$

(B) $x+2y-5=0$

(D) $x-2y+1=0$

Q23

If $p$ is the length of the perpendicular from origin to the line $ax+by+c=0$, then $p=$
(Exam: NEET Year: 2019)

(A) $\frac{c}{\sqrt{a^2+b^2}}$

(B) $\frac{|c|}{\sqrt{a^2+b^2}}$

(D) $\sqrt{a^2+b^2}$

Q24

The pair of lines represented by $x^2-y^2=0$ are
(Exam: IIT-JEE Year: 1997)

(A) $x+y=0,\;x-y=0$

(B) $x=0,\;y=0$

(D) $x= y^2$

Q25

The acute angle between the lines $3x-4y+5=0$ and $4x+3y-7=0$ is
(Exam: JEE Advanced Year: 2014)

(A) $30^\circ$

(B) $45^\circ$

(D) $90^\circ$

Q26

The equation of the line whose intercepts on the axes are in the ratio $2:3$ and whose sum is $10$ is
(Exam: BITSAT Year: 2012)

(A) $3x+2y=12$

(B) $3x+2y=10$

(D) $2x+3y=12$

Q27

The condition for the lines $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$ to be perpendicular is
(Exam: JEE Main Year: 2010)

(A) $a_1a_2+b_1b_2=0$

(B) $a_1b_2-a_2b_1=0$

(D) $c_1=c_2$

Q28

The equation of the line through $(2,1)$ making equal intercepts on the axes is
(Exam: NEET Year: 2016)

(A) $x+y-3=0$

(B) $x-y-1=0$

(D) $x+2y-4=0$

Q29

If the area of the triangle formed by the coordinate axes and the line $ax+by=1$ is $2$, then $ab=$
(Exam: IIT-JEE Year: 2003)

(A) $\frac{1}{2}$

(B) $\frac{1}{4}$

(D) $2$

Q30

The image of the point $(3,4)$ in the line $x-y=0$ is
(Exam: Olympiad Year: 2006)

(A) $(4,3)$

(B) $(-3,-4)$

(D) $(-4,3)$

Q31

The slope of the angle bisectors of the lines $y=x$ and $y=-x$ are
(Exam: JEE Advanced Year: 2017)

(A) $0,\infty$

(B) $1,-1$

(D) $\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}$

Q32

The equation of the line joining the midpoints of the sides of the triangle formed by the axes and the line $x+y=6$ is
(Exam: IIT-JEE Year: 2000)

(A) $x+y=3$

(B) $x+y=6$

(D) $x+y=0$

Q33

The line $ax+by+c=0$ passes through $(1,2)$ and is perpendicular to $x+3y-7=0$. Then $\frac{a}{b}=$
(Exam: NEET Year: 2021)

(A) $-3$

(B) $3$

(D) $\frac{1}{3}$

Q34

The equation of the line passing through origin and making an angle $30^\circ$ with the line $y=x$ is
(Exam: JEE Advanced Year: 2012)

(A) $y=(2+\sqrt{3})x$

(B) $y=(\sqrt{3}-1)x$

(D) $y=\frac{1}{\sqrt{3}}x$

Q35

The equation of the director circle of the pair of lines $x^2-y^2=0$ is
(Exam: IIT-JEE Year: 2004)

(A) $x^2+y^2=0$

(B) $x^2+y^2=1$

(D) $x^2-y^2=0$

Q36

The equation of the line through $(1,2)$ such that the intercept between the axes is bisected at that point is
(Exam: JEE Advanced Year: 2015)

(A) $x+2y-5=0$

(B) $2x+y-5=0$

(D) $2x+2y-6=0$

Q37

The distance between the parallel lines $3x+4y+5=0$ and $3x+4y-5=0$ is
(Exam: NEET Year: 2015)

(A) $1$

(B) $2$

(D) $2$

Q38

The number of lines that can be drawn through the point $(1,1)$ making intercepts on axes whose product is constant is
(Exam: Olympiad Year: 2009)

(A) 1

(B) 2

(D) none

Q39

The equation of the line passing through the point of intersection of $x=1$ and $y=2$ and parallel to $3x-y=5$ is
(Exam: JEE Main Year: 2018)

(A) $3x-y-1=0$

(B) $3x-y+1=0$

(D) $y-3x+1=0$

Q40

If the line $y=mx+c$ passes through $(2,3)$ and $(4,7)$, then $m+c=$
(Exam: BITSAT Year: 2011)

(A) 2

(B) 3

(D) 5

Q41

The locus of the foot of the perpendicular drawn from origin to a variable line passing through $(a,0)$ is
(Exam: IIT-JEE Year: 2006)

(A) circle

(B) parabola

(D) straight line

Q42

The equation of the line through $(1,1)$ that cuts off equal intercepts on the axes is
(Exam: NEET Year: 2014)

(A) $x+y=2$

(B) $x-y=0$

(D) $x+2y=3$

Q43

The condition that the line $ax+by+1=0$ touches the circle $x^2+y^2=4$ is
(Exam: JEE Advanced Year: 2016)

(A) $a^2+b^2=1$

(B) $a^2+b^2=\frac{1}{4}$

(D) $a^2+b^2=4$

Q44

The equation of the median of the triangle with vertices $(0,0),(2,0),(0,2)$ through $(0,0)$ is
(Exam: JEE Main Year: 2017)

(A) $x-y=0$

(B) $x+y=0$

(D) $x-2y=0$

Q45

The angle between the lines $x=0$ and $x\cos\theta+y\sin\theta=0$ is
(Exam: IIT-JEE Year: 1996)

(A) $\theta$

(B) $\frac{\pi}{2}-\theta$

(D) $\tan^{-1}\theta$

Q46

The line joining the points where $x^2-y^2=0$ meets the circle $x^2+y^2=8$ is
(Exam: Olympiad Year: 2011)

(A) $y=0$

(B) $x=0$

(D) $x-y=0$

Q47

The equation of the line through $(1,2)$ whose distance from origin is minimum is
(Exam: JEE Advanced Year: 2018)

(A) $2x-y=0$

(B) $x-2y=0$

(D) $x+2y-5=0$

Q48

The slope of the line joining the points where $x+y=4$ cuts the axes is
(Exam: NEET Year: 2022)

(A) $-1$

(B) $1$

(D) undefined

Q49

The equation of the angle bisectors of the lines $x^2-5xy+6y^2=0$ are
(Exam: JEE Advanced Year: 2019)

(A) $x=0,y=0$

(B) $x-2y=0,x-3y=0$

(D) $x-y=0$

Q50

The line which is the locus of the midpoints of chords of the circle $x^2+y^2=9$ passing through $(3,0)$ is
(Exam: IIT-JEE Year: 2002)

(A) $x= \frac{3}{2}$

(B) $y=0$

(D) $x-3=0$

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