﻿ If the area of the quadrilateral formed by the tangent from the origin to the circle x2 + y2 + 6x – 10y + c = 0 and the pair of radii at the points of contact of these tangents to the circle is 8 square units, then c is a root of the equation : Kaysons Education

# If The Area Of The Quadrilateral Formed By The Tangent From The Origin To The Circle x2 + y2 + 6x – 10y + c = 0 And The Pair Of Radii At The Points Of Contact Of These Tangents To The Circle Is 8 Square Units, Then c is A Root Of The Equation

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## Question

### Solution

Correct option is

c2 – 34c + 64 = 0

Let OAOB be the tangents from the origin to the given circle with centre C(–3, 5) and radius

Then area of the quadrilateral OACB = 2 × area of the triangle OAC

Now OA = length of the tangent from the origin to the given circle

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