Mathematics Coordinate Geometry questions from JEE Main 2015.
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 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:
An ellipse passes through the foci of the hyperbola, $9{x}^{2}-4{y}^{2}=36$ and its major and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is $\frac{1}{2},$ then which of the following points does not lie on the ellipse?