JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
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
- A \(x^2 +y^2 + 3x + 9y = 0\)
- B \(x^2 +y^2 + 3x - 9y = 0\)
- C \(x^2 +y^2 - 3x - 9y = 0\)
- D \(x^2 +y^2 - 3x + 9y = 0\)
Answer & Solution
Correct Answer
(D) \(x^2 +y^2 - 3x + 9y = 0\)
Step-by-step Solution
Detailed explanation
given that \(y+3x=0 \) is the equation of a chord of the circle then \(y=-3x\) ......\((i)\) \(\left( {{x^2}} \right) + {\left( { - 3x} \right)^2} - 30x = 0\) \(10{x^2} - 30x = 0\) \(10x\left( {x - 3} \right) = 0\) \(x = 0,y = 0\) so the equation of the circle is…
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