JEE Main 2015 · 10 Apr · Shift 1 · Mathematics Q80

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MathematicsSingle correct+4 / -1Question 80 of 90

If $y+3x=0$ is the equation of a chord of the circle, $x^2+y^2-30x=0$ , then the equation of the circle with this chord as diameter is :

x^2+y^2+3x+9y=0

x^2+y^2-3x+9y=0

x^2+y^2-3x-9y=0

x^2+y^2+3x-9y=0

Answer and worked solution

Official answer: B

The chord meets the circle where $x^2+9x^2-30x=0$ : $x=0$ or $x=3$ , i.e. the points (0, 0) and (3, −9). With these as diameter:
$x(x-3)+y(y+9)=0\iff x^2+y^2-3x+9y=0.$

Topics:Equation of a circle

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JEE Main 2015 · 10 Apr · Shift 1, Mathematics question 80