﻿ The circle x2 + y2 = 1 cuts the x-axis at P and Q. another circle with centre at Q and variable radius intersects the first circle at R above the x-axis and the line segment PQ at S. Find the maximum area of the triangleQSR. : Kaysons Education

# The Circle x2 + y2 = 1 Cuts The x-axis At P and Q. Another Circle With Centre At Q and Variable Radius Intersects The First Circle At R above The x-axis And The Line Segment PQ at S. Find The Maximum Area Of The TriangleQSR.

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## Question

### Solution

Correct option is

The given circle is                 x2 + y2 = 1

With centre at O (0, 0) and radius 1. It cuts x-axis at the points when y = 0 then x = ± 1 i.e., at P(–1, 0) and Q(1, 0).

Equation of circle with centre at Q(1, 0) and radius r is

(x – 1)2 + (y – 0)2 = r2         …(2)           (0 < r < 2)

Solving (1) and (2), we get

But above the x-axis.

For maximum and minimum area,

∴ A is maximum. Hence âˆ† is also maximum.

#### SIMILAR QUESTIONS

Q1

Find the equations of the circle which passes through the origin and cut off chords of length a from each of the lines y = x and y = –x.

Q2

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Q3

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Q5

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Q6

Find the radius of smaller circle which touches the straight line 3x – y = 6 at (1, –3) and also touches the line y = x.

Q7

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Q8

Let 2x2 + y2 – 3xy = 0 be the equation of a pair of tangents drawn from the origin O to a circle of radius 3 with centre in the first quadrant. If A is one of the points of contact, find the length of OA.

Q9

If the circle C1x2 + y2 = 16 intersects another circle C2 of radius 5 in such a manner that the common chord is of maximum length and has a slope equal to (3/4), find the co-ordinates of centre C2.

Q10

Find the equation of a circle having the lines x2 + 2xy + 3x + 6y = 0 as its normals and having size just sufficient to contain the circle

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