Class 11

Math

Co-ordinate Geometry

Conic Sections

If the straight line $xcosα+ysinα=p$ touches the curve $a_{2}x_{2} +b_{2}y_{2} =1$ , then prove that $a_{2}cos_{2}α+b_{2}sin_{2}α=p_{2}˙$

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Find the equation of the parabola with vertex at (0, 0) and focus at (0, 2).

If the midpoints of the sides of a triangle are $(2,1),(−1,−3),and(4,5),$ then find the coordinates of its vertices.

Let $A=(3,4)$ and $B$ is a variable point on the lines $∣x∣$ =6. IF $AB≤4$ , then find the number of position of $B$ with integral coordinates.

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.$100x_{2} +400y_{2} =1$

For what value of $k$ are the points $(k,2−2k),(−k+1,2k)and(−4−k,6−2k)$ collinear?

The focus of a parabolic mirror as shown in is at a distance of 5 cm from its vertex. If the mirror is 45 cm deep, find the distance AB

The line joining the points $(x,2x)and(3,5)$ makes an obtuse angle with the positive direction of the x-axis. Then find the values of $x˙$

Find the equations of the hyperbola satisfying the given conditions :Vertices $(±2,0),foci(±3,0)$