If the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$ is touched by $y = x$ at $P$ such that $OP = 6\sqrt 2 ,$ then the value of $c$ is

JEE MATHEMATICS MCQ: CIRCLES

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Application +4 | -1

If the circle

{x^2} + {y^2} + 2gx + 2fy + c = 0

is touched by

y = x

P

such that

OP = 6\sqrt 2 ,

then the value of

c

View answer and explanation

Correct option: C

Option C (72) is correct because by substituting the point and using the tangency condition, we can derive the value of 'c' as 72.

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{\left( {{\alpha ^2}{x^2} - 2\alpha \mathrm{ }x + 1} \right)^{51}},

x

\left( {\alpha ,2{\alpha ^2}} \right)

{x^2} + {y^2} = 4,

{x^2} + {y^2} - 2x + 4y - 4 = 0

{x^2} + {y^2} = {a^2}

\left( {{x_1},{y_1}} \right)

\quad \alpha, \beta

\gamma

P, Q

x^2+y^2=1

A

(-1,0)

A P, A Q

A R

G P

\cos \alpha / 2, \cos \beta / 2

\cos \gamma / 2

x+y=6

x+2 y=4

x+y=5

x-y=1

9 \pi