﻿ If a rectangular hyperbola whose center is C, is cut by any circle of radiusr in the four points P, Q, R, S, then  CP2 + CQ2 + CR2 + CS2 = : Kaysons Education

# If A Rectangular Hyperbola Whose Center Is C, Is Cut By Any Circle Of Radiusr in The Four Points P, Q, R, S, Then  CP2 + CQ2 + CR2 + CS2 =

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## Question

### Solution

Correct option is

4r2

Circle is x2 + y2 + 2gx + 2fy + d = 0              ……. (1)

Its radius = r ⇒ r2 = g2 + f2 – d                     …… (2)

Rectangular hyperbola as xy = c2                 …… (3)

Whose center is at (0, 0). Take , a point on (2).

Put this in (1).

⇒ c2t4 + 2gct3 + 2fct + dt2 + c= 0                 …… (3)

(3) Gives point of intersections

Now

Here

.     by   (3)

….. (4)

Similarly if we replace

….. (5)

#### SIMILAR QUESTIONS

Q1

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Q2

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Q3

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Q4

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Q5

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Q6

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Q7

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Q8

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Q9

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Q10

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