JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
Let the lines \(y+2 x=\sqrt{11}+7 \sqrt{7}\) and \(2 y + x =2 \sqrt{11}+6 \sqrt{7}\) be normal to a circle \(C:(x-h)^{2}+(y-k)^{2}=r^{2}\). If the line \(\sqrt{11} y -3 x =\frac{5 \sqrt{77}}{3}+11\) is tangent to the circle \(C\), then the value of \((5 h-8 k)^{2}+5 r^{2}\) is equal to.......
- A \(916\)
- B \(816\)
- C \(856\)
- D \(86\)
Answer & Solution
Correct Answer
(B) \(816\)
Step-by-step Solution
Detailed explanation
Normal are \(y +2 x =\sqrt{11}+7 \sqrt{7}\) \(2 y + x =2 \sqrt{11}+6 \sqrt{7}\) Center of the circle is point of intersection of ormals i.e. \(\left(\frac{8 \sqrt{7}}{3}, \sqrt{11}+\frac{5 \sqrt{7}}{3}\right)\) Tangent is \(\sqrt{11} y-3 x=\frac{5 \sqrt{77}}{3}+11\) Radius will…
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