Question

The length of the y-intercept made by the circle x 2 + y 2 – 8x + y – 20 = 0 is

Answer 1

SOLUTION

TO DETERMINE

The length of the y-intercept made by the circle

$\sf{ {x}^{2} + {y}^{2} - 8x + y - 20 = 0 }$

EVALUATION

Here the given equation of the circle is

$\sf{ {x}^{2} + {y}^{2} - 8x + y - 20 = 0 }$

Comparing with the general equation of a circle

$\sf{a {x}^{2} + b{y}^{2} + 2gx +2f y + c = 0 }$

We have

a = 1 , b = 1 , 2g = - 8 , 2f = 1 , c = - 20

Hence the required y-intercept

$= \sf{2 \sqrt{ {f}^{2} - c }}$

$= \sf{ \sqrt{ 4{f}^{2} - 4c }}$

$= \sf{ \sqrt{ {(2f)}^{2} - 4c }}$

$= \sf{ \sqrt{ {(1)}^{2} - 4 \times ( - 20)}}$

$= \sf{ \sqrt{ 1 + 80}}$

$= \sf{ \sqrt{ 81}}$

$= \sf{9}$

FINAL ANSWER

Hence the required y-intercept = 9 unit

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