JEE Main Mathematics — Coordinate Geometry previous year questions with solutions.
If the tangent to the conic, $y-6={x}^{2}$ at $(2,10)$ touches the circle, ${x}^{2}+{y}^{2}+8x-2y=k$ (for some fixed $k$) at a point $(\alpha , \beta );$ then $(\alpha , \beta )$ is
If $y+3x=0$ is the equation of a chord of the circle ${x}^{2}+{y}^{2}-30x=0$, then the equation of the circle with this chord as diameter is :
The points $(0,\frac{8}{3}),(1,3)$ and $(82,30)$
The number of common tangents to the circles ${x}^{2} + {y}^{2} - 4 x - 6 y - 1 2 = 0$ and ${x}^{2}+{y}^{2}+6x+18y+26=0$, is
If $PQ$ be a double ordinate of the parabola, ${y}^{2}=-4x,$ where $P$ lies in the second quadrant. If $R$divides $PQ$ in the ratio $2:1,$ then the locus of $R$ is:
If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is:
Let $L$ be the line passing through the point $P(1,2)$ such that its intercepted segment between the co-ordinate axes is bisected at $P$. If ${L}_{1}$ is the line perpendicular to $L$ and passing through the point $(-2,1)$, then the point of intersection of $L$ and ${L}_{1}$ is
If a circle passing through the point $(-1,0)$ touches $y$-axis at $(0,2)$, then the $x$-intercept of the circle is
Let the tangents drawn to the circle, ${x}^{2}+{y}^{2}=16$ from the point$P(0,h)$ meet the $x$-axis at points $A$ and $B$. If the area of $\Delta APB$ is minimum, then positive value of $h$ is:
The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latus ractum to the ellipse $\frac{{x}^{2}}{9}+\frac{{y}^{2}}{5}=1,$ is
Locus of the image of the point $( 2,3 )$ in the line $( 2 x - 3 y + 4 ) + k ( x - 2 y + 3 ) = 0 , k \in R ,$ is a
A straight line $L$ through the point $(3, -2)$ is inclined at an angle of $60^{\circ}$ to the line $\sqrt{3}x+y=1.$ If $L$ also intersects the $X$-axis, then the equation of $L$ is:
Let $O$ be the vertex and $Q$ be any point on the parabola, ${x}^{2}=8y$. If the point $P$ divides the line segment $OQ$ internally in the ratio $1:3$, then the locus of $P$ is
If $OB$ is the semi-minor axis of an ellipse, ${F}_{1}$ and ${F}_{2}$ are its focii and the angle between ${F}_{1}B$ and ${F}_{2}B$ is a right angle, then the square of the eccentricity of the ellipse is
Given three points $P,Q,R$ with $P(5,3)$ and $R$ lies on the $x-$axis. If the equation of $RQ$ is $x-2y=2$ and $PQ$ is parallel to the $x-$axis, then the centroid of $\Delta PQR$ lies on the line
A chord is drawn through the focus of the parabola ${ y }^{2} = 6 x$ such that its distance from the vertex of this parabola is $\frac{ \sqrt{ 5 } }{ 2 }$, then its slope can be
A stair-case of length $l$ rests against a vertical wall and a floor of a room. Let $\mathrm{P}$ be a point on the stair-case, nearer to its end on the wall, that divides its length in the ratio $1: 2$. If the staircase begins to slide on the floor, then the locus of $\mathrm{P}$ is:
If a line intercepted between the coordinate axes is trisected at a point $\mathrm{A}(4,3)$, which is nearer to $x$-axis, then its equation is:
The circumcentre of a triangle lies at the origin and its centroid is the midpoint of the line segment joining the points $({a}^{2}+1,{a}^{2}+1)$ and $(2a, - 2a),a\neq 0$. Then for any $a,$ the orthocentre of this triangle lies on the line
For the two circles $x^2+y^2=16$ and $x^2+y^2-2 y=0$, there is/are
The set of all real values of $\lambda$ for which exactly two common tangents can be drawn to the circles $x^2+y^2-4 x-4 y+6=0$ and $\mathrm{x}^2+\mathrm{y}^2-10 \mathrm{x}-10 \mathrm{y}+\lambda=0$ is the interval:
Let $\mathrm{L}_1$ be the length of the common chord of the curves $x^2+y^2=9$ and $y^2=8 x$, and $L_2$ be the length of the latus rectum of $y^2=8 x$, then:
If the point $(1,4)$ lies inside the circle ${x}^{2}+{y}^{2}-6x+10y+p=0$ and the circle does not touch or intersect the coordinate axes, then the set of all possible values of $p$ is the interval
Let $a$ and $b$ be any two numbers satisfying $\frac{1}{{a}^{2}}+\frac{1}{{b}^{2}}=\frac{1}{4}.$ Then, the foot of perpendicular from the origin on the variable line $\frac{x}{a}+\frac{y}{b}=1$ lies on :