Class 11

Math

Co-ordinate Geometry

Conic Sections

The moon travels an elliptical path with Earth as one focus. The maximum distance from the moon to the earth is 405, 500 km and the minimum distance is 363,300 km. What is the eccentricity of the orbit?

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If the point $(2,3),(1,1),and(x,3x)$ are collinear, then find the value of $x,$ using slope method.

If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

In Fig. 10.39, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that $∠BEC=130o$ and $∠ECD=20⊙$ Find $∠BAC˙$

Convert $y=10$ into a polar equation.

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.$16x_{2}+y_{2}=16$

If $A(x_{1},y_{1}),B(x_{2},y_{2}),$ and $C(x_{3},y_{3})$ are three non-collinear points such that $x12+y12=x22+y22=x32+y32,$ then prove that $x_{1}sin2A+x_{2}sin2B+x_{3}sin2C=y_{1}sin2A+y_{2}sin2B+y_{3}sin2C=0.$

Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.$5y_{2}−9x_{2}=36$

Find the equation of the circle with centre :(0, 2) and radius 2