Find the radius of the circle x2-y2-2 x-4 y-11-0A- 4

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Standard X

Mathematics

Equation of the Circle Using End Points of Diameter

Find the radi...

Question

Find the radius of the circle $x^{2} + y^{2} - 2 x + 4 y - 11 = 0$ .
4

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Solution

The correct option is A 4
Equation of a circle with radius 'r' and center (a, b) is $(x - a)^{2} + (y - b)^{2} = r^{2}$
.
We have to convert the given equation in the above format.

Given,
$x^{2} + y^{2} - 2 x + 4 y - 11 = 0 x^{2} - 2 x + y^{2} + 4 y = 11 x^{2} - 2 x + 1 + y^{2} + 4 y + 4 = 16 (x - 1)^{2} + (y + 2)^{2} = 4^{2}$

Comparing these equations, we get r = 4.

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Find the radius of the circle x2 + y2 − 2x + 4y − 11 = 0.4

The correct option is A 4Equation of a circle with radius 'r' and center (a, b) is (x−a)2+(y−b)2=r2 . We have to convert the given equation in the above format. Given, x2 + y2 − 2x + 4y − 11 = 0x2−2x+y2+4y=11x2−2x+1+y2+4y+4=16(x−1)2+(y+2)2=42 Comparing these equations, we get r = 4.

Find the radius of the circle $x^{2} + y^{2} - 2 x + 4 y - 11 = 0$ .
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