JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
The absolute difference between the squares of the radii of the two circles passing through the point \((-9,4)\) and touching the lines \(x+y=3\) and \(x-y=3\), is equal to ______.
- A 768
- B 767
- C 766
- D 735
Answer & Solution
Correct Answer
(A) 768
Step-by-step Solution
Detailed explanation
Centre \((\mathrm{a}, 0)\) \(\mathrm{r}=\left|\frac{\mathrm{a}-0-3}{\sqrt{2}}\right|\) \(\operatorname{circle}(x-a)^2+y^2=\left(\frac{a-3}{\sqrt{2}}\right)^2\) passes through \((-9,4)\) \(2\left(a^2+18 a+81+16\right)=\left(a^2-6 a+9\right)\) \(\mathrm{a}^2+42 \mathrm{a}+185=0\)…
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