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STD 11 - 10.1 circle and system of circle — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 10.1 circle and system of circle1 Mark
MCQ
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 $\left(a^{2}+b^{2}+a b\right)$ is equal to ..... .
  • A
    $6$
  • B
    $3$
  • C
    $4$
  • ✓
    $9$
✓

Answer

Correct option: D.
$9$
d
All normals of circle passes through centre Radius $= CA = CB$

$CA ^{2}= CB ^{2}$

$( a -3)^{2}+( b +3)^{2}$

$=( a -4)^{2}+( b -2 \sqrt{2})^{2}$

$a+(3-2 \sqrt{2}) b=3$

$a-2 \sqrt{2} b+3 b=3 ....(1)$

given that $a -2 \sqrt{2} b =3 ....(2)$

from $(1) \&(2) \Rightarrow a=3, b=0$

$a^{2}+b^{2}+a b=9$

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