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Sum of Opposite Angles of a Cyclic Quadrilateral

ntProve that ...

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ntProve that the parabola y2=16x and the circle x2 + y2 -40x-16y-48=0 meet at point P(36,24) and one another point Q. Prove that PQ is diameter of the circle. Find Q.n

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Q. The two circles

x^{2} + y^{2} + 2 a x - c^{2} = 0

x^{2} + y^{2} + 2 a b x - c^{2} = 0

meet in points P and Q. Parallel lines are drawn through P and Q meet the circles in point R and S. Prove that the locus of mid-point of RS is the circle.

x^{2} + y^{2} + (a + b) x = 0

x^{2} + y^{2} = 5

meets the parabola

y^{2} = 4 x

P

Q

. Then the length

P Q

Q. Prove that , the normal to

y^{2} = 12 x

at (3,6) meets the parabola again in

(27, - 18)

& circle on this normal chord as diameter is

x^{2} + y^{2} - 30 x + 12 y - 27 = 0

x^{2} + y^{2} - 6 x + 4 y - 7 = 0

x^{2} + y^{2} - 16 x - 6 y + 63 = 0

intersect at the points p and q. Find the equation of the line pq.

Q. The equation of a circle whose radius is

8

units and which touches both

x -

y -

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Sum of Opposite Angles of a Cyclic Quadrilateral

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