Class 12

Math

Co-ordinate Geometry

Conic Sections

Sum of slopes of common tangent to $y=4x_{2} −3x+10$ and $y=2−4x_{2} $ is

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Find the angle between the pair of tangents from the point (1,2) to the ellipse $3x_{2}+2y_{2}=5.$

Find the equation of the parabola that satisfies the following conditions: Vertex $(0,0)$ passing through $(2,3)$ and axis is along $x$-axis

If from a point $P,$ tangents $PQandPR$ are drawn to the ellipse $2x_{2} +y_{2}=1$ so that the equation of $QR$ is $x+3y=1,$ then find the coordinates of $P˙$

Find the slope of a common tangent to the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ and a concentric circle of radius $r˙$

Prove that the area bounded by the circle $x_{2}+y_{2}=a_{2}$ and the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ is equal to the area of another ellipse having semi-axis $a−b$ and $b,a>b$ .

The point of intersection of the tangents at the point $P$ on the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$ and its corresponding point $Q$ on the auxiliary circle meet on the line (a) $x=ea $ (b) $x=0$ (c) $y=0$ (d) none of these

Find the equation of the parabola that satisfies the following conditions: Focus $(0,−3)$; directrix $y=3$

If $PSQ$ is a focal chord of the ellipse $16x_{2}+25y_{2}=400$ such that $SP=8,$ then find the length of $SQ.$ is (a) $21 $ (b) $94 $ (c) $98 $ (d) $916 $