CIRCLE X2 + y2 = a2.(h, k) will satisfy the EQUATION x2 + y2 = a2.⇒ h2 + k2 = a2 The equation of the chord of the contact of tangents drawn from the point P(h, k) to the circle x2 + y2 = b2 will behx + ky = b2 Perpendicular distance of this tangent from the centre of the circle x2 + y2 = c2 will be equal to the RADIUS of the circle.\(⇒ |{-b^2 \over \sqrt{h^2+k^2}}| = c\)\(⇒ |{-b^2 \over a}| = c\)\(⇒ b^2 = ac\)Comparing it with BP = amcn ⇒ p = 2, m = n = 1∴ m + n + p + 3 = 1 + 1 + 2 + 3 = 7

"> CIRCLE X2 + y2 = a2.(h, k) will satisfy the EQUATION x2 + y2 = a2.⇒ h2 + k2 = a2 The equation of the chord of the contact of tangents drawn from the point P(h, k) to the circle x2 + y2 = b2 will behx + ky = b2 Perpendicular distance of this tangent from the centre of the circle x2 + y2 = c2 will be equal to the RADIUS of the circle.\(⇒ |{-b^2 \over \sqrt{h^2+k^2}}| = c\)\(⇒ |{-b^2 \over a}| = c\)\(⇒ b^2 = ac\)Comparing it with BP = amcn ⇒ p = 2, m = n = 1∴ m + n + p + 3 = 1 + 1 + 2 + 3 = 7

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The chord of the contact of tangents drawn from a point on the circle x2 + y2 = a2 to the circle x2 + y2 = b2 touches the circle x2 + y2 = c2 such that bp = amcn, where m, n, p ϵ N, and m, n, p are prime to each other, then the value of m + n + p + 3 is:

General Knowledge General Awareness in General Knowledge 9 months ago

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Let there is a point P(h, k) on the CIRCLE X2 + y2 = a2.(h, k) will satisfy the EQUATION x2 + y2 = a2.⇒ h2 + k2 = a2 The equation of the chord of the contact of tangents drawn from the point P(h, k) to the circle x2 + y2 = b2 will behx + ky = b2 Perpendicular distance of this tangent from the centre of the circle x2 + y2 = c2 will be equal to the RADIUS of the circle.\(⇒ |{-b^2 \over \sqrt{h^2+k^2}}| = c\)\(⇒ |{-b^2 \over a}| = c\)\(⇒ b^2 = ac\)Comparing it with BP = amcn ⇒ p = 2, m = n = 1∴ m + n + p + 3 = 1 + 1 + 2 + 3 = 7

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Posted on 12 Nov 2024, this text provides information on General Knowledge related to General Awareness in General Knowledge. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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