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Straight Lines and Pair of Straight Lines

563 Questions
All Exams JEE Mains JEE Advanced TS-EAMCET AP-EAPCET
1983 JEE Advanced Numerical
IIT-JEE 1983
The coordinates of $A, B, C$ are $(6, 3), (-3, 5), (4, -2)$ respectively, and $P$ is any point $(x, y)$. Show that the ratio of the area of the triangles $\Delta $ $PBC$ and $\Delta $$ABC$ is $\left| {{{x + y - 2} \over 7}} \right|$
1983 JEE Advanced Numerical
IIT-JEE 1983
Given the points $A\left( {0,4} \right)$ and $B\left( {0, - 4} \right)$, the equation of the locus of the point $P\left( {x,y} \right)$ such that $\left| {AP - BP} \right| = 6$ is .............
1983 JEE Advanced MCQ
IIT-JEE 1983
The straight line $5x + 4y = 0$ passes through the point of intersection of the straight lines $x + 2y - 10 = 0$ and $2x + y + 5 = 0.$
A.
TRUE
B.
FALSE
1982 JEE Advanced Numerical
IIT-JEE 1982
$y = {10^x}$ is the reflection of ${\log _{10}}\,x$ in the line whose equation is ...........
1982 JEE Advanced Numerical
IIT-JEE 1982
The set of lines $ax + by + c = 0,$ where $3a + 2b + 4c = 0$ is concurrent at the point ..........
1981 JEE Advanced Numerical
IIT-JEE 1981
The area enclosed within the curve $\left| x \right| + \left| y \right| = 1$ is .................
1980 JEE Advanced MCQ
IIT-JEE 1980
The point $\,\left( {4,\,1} \right)$ undergoes the following three transformations successively.
Reflection about the line $y=x$.
Translation through a distance 2 units along the positive direction of x-axis.
Rotation through an angle $p/4$ about the origin in the counter clockwise direction.
Then the final position of the point is given by the coordinates.
A.
$\left( {{1 \over {\sqrt 2 }},{7 \over {\sqrt 2 }}} \right)$
B.
$\left( { - \sqrt 2 ,\,7\sqrt 2 } \right)$
C.
$\left( { - {1 \over {\sqrt 2 }},{7 \over {\sqrt 2 }}} \right)$
D.
$\left( { \sqrt 2 ,\,7\sqrt 2 } \right)$
1980 JEE Advanced Numerical
IIT-JEE 1980
A straight line $L$ is perpendicular to the line $5x - y = 1.$ The area of the triangle formed by the line $L$ and the coordinate axes is $5$. Find the equation of the Line $L$.
1979 JEE Advanced MCQ
IIT-JEE 1979
The points $\left( { - a,\, - b} \right),\,\left( {0,\,0} \right),\,\left( {a,\,b} \right)$ and $\left( {{a^2},\,ab} \right)$ are :
A.
Collinear
B.
Vertices of a parallelogram
C.
Vertices of a rectangle
D.
None of these
1979 JEE Advanced Numerical
IIT-JEE 1979
(a) Two vertices of a triangle are $(5, -1)$ and $(-2, 3).$ If the orthocentre of the triangle is the origin, find the coordinates of the third point.
(b) Find the equation of the line which bisects the obtuse angle between the lines $x - 2y + 4 = 0$ and $4x - 3y + 2 = 0$.
1978 JEE Advanced Numerical
IIT-JEE 1978
A straight line segment of length $\ell $ moves with its ends on two mutually perpendicular lines. Find the locus of the point which divides the line segment in the ratio $1 : 2$
1978 JEE Advanced Numerical
IIT-JEE 1978
One side of rectangle lies along the line $4x + 7y + 5 = 0.$ Two of its vertices are $(-3, 1)$ and $(1, 1).$ Find the equations of the other three sides.
1978 JEE Advanced Numerical
IIT-JEE 1978
The area of a triangle is $5$. Two of its vertices are $A\left( {2,1} \right)$ and $B\left( {3, - 2} \right)$. The third vertex $C$ lies on $y = x + 3$. Find $C$.