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  • Let the normals at all the points on a given curve pass through a fixed point (a,b). If the curve passes through (3,-3) and  and given

Let the normals at all the points on a given curve pass through a fixed point (a,b). If the curve passes through (3,-3) and (4,-2\sqrt{2}) and given that a-2\sqrt{2}b =3, then (a^2+b^2+ab) is equal to ________
Option: 1 9
Option: 2 10
Option: 3 5
Option: 4 7

Answers (1)

best_answer

All normals of a circle pass through center Radius = CA = CB

\\\mathrm{CA^2=CB^2}\\ (a-3)^{2}+(b+3)^{2} =(a-4)^{2}+(b-2 \sqrt{2})^{2} \\ a+(3-2 \sqrt{2}) b=3 \\ a-2 \sqrt{2} b+3 b=3 \\ \text { given that } a-2 \sqrt{2} b=3\\ \text{from above, we get }a=3 \text{ and }b=0\\a^{2}+b^{2}+a b=9

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