Question

║⊕QUESTION⊕║
Pure mathematics is, in its way, the poetry of logical ideas.
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CLASS 11
CIRCLE
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The intercept of the line y = x by the circle $x^{2} + y^{2} - 2x = 0$ is AB. Equation of circle on AB as diameter is
$a) x^{2} + y^{2} + x + y = 0\\b) x^{2} + y^{2} - x + y = 0\\c) x^{2} + y^{2} - (x+y) = 0\\d) x^{2} + y^{2} + x - y = 0$

Answer 1

◆【SOLUTION】◆

Equation of line....

y = x

Equation of circle....

x² + y² - 2x = 0

Solve both equations put first equation in second....

x² + x² - 2x = 0

2x² - 2x = 0

2x(x - 1) = 0

Hence X coordinate of A and B is 0,1

And we know that x = y equation of line satisfied by these point so we get the point...

◆【A = (0,0)】◆

◆【B = (1,1) 】◆

If the extremities of diameter is (a,b) and (c,d)

Than equation of the circle can be written as

(x - a)(x - c) + (y - b)(y - d) = 0

So using this we get the equation of circle with extremities of diameter as A and B

(x - 0)(x - 1) + (y - 0)(y - 1) = 0

x(x -1) + (y - 1)y = 0

x² + y² - x - y = 0

◆【x² + y² - (x + y) = 0】◆

#answerwithquality

#BAL

Answer 2

Answer:

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