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Sum of Infinite Terms

if the line ...

Question

if the line px +qy+r=0 touches the circle x^2 +y^2=a^2 then show that r^{2 }=a^2(p^2+q^2).

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If $p x + q y + r = 0$ is tangent of the parabola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ then

p x + q y = 1

touches the circle

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

, Prove that the point

(p, q)

lies on the circle

x^{2} + y^{2} = r^{- 2}

Q. Find the condition for the line

p x + q y + r = 0

to touch the circle

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

. Also find the co-ordinates of the point of contact.

l x + m y + n = 0

touches the circle

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

, then prove that

(l^{2} + m^{2}) a^{2} = n^{2}

Q. The pole of a straight line with repect to the circle

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

lies on the circle

x^{2} + y^{2} = 9 a^{2} .

Prove that the straight line touches the circle

x^{2} + y^{2} = a^{2} / 9.

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Sum of Infinite Terms

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