JEE Main 2015 — Coordinate Geometry

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 $y+3x=0$ 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 :

If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is:

If the incentre of an equilateral triangle is $(1,1)$ and the equation of its one side is $3x+4y+3=0$, then the equation of the circumcircle of this triangle is:

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

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

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

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:

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

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

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

The points $(0,\frac{8}{3}),(1,3)$ and $(82,30)$