JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
Let \(C\) be a circle having centre in the first quadrant and touching the \(x\)-axis at a distance of \(3\) units from the origin. If the circle \(C\) has an intercept of length \(6\sqrt{3}\) on \(y\)-axis, then the length of the chord of the circle \(C\) on the line \(x - y = 3\) is :
- A \(8\)
- B \(6\)
- C \(6\sqrt{2}\)
- D \(8\sqrt{2}\)
Answer & Solution
Correct Answer
(C) \(6\sqrt{2}\)
Step-by-step Solution
Detailed explanation
Let the centre of the circle be \((3, r)\) since it touches the \(x\)-axis at \((3, 0)\) and lies in the first quadrant. The radius of the circle is \(r\). The length of the intercept on the \(y\)-axis is given by \(2\sqrt{r^2 - d^2}\), where \(d\) is the distance of the centre…
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