Class 11

Math

Co-ordinate Geometry

Conic Sections

The locus a point $P(α,β)$ moving under the condition that the line $y=αx+β$ is a tangent to the hyperbola $a_{2}x_{2} −b_{2}y_{2} =1$ is (A) a parabola (B) an ellipse (C) a hyperbola (D) a circle

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$XY$and $XprimeYprime$are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting $XY$at A and $XprimeYprime$at B. Prove that $∠AOB=90o$

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An arch is in the form of a semi–ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.