If a chord of contact of tangents drawn from a point $P$ with respect to the circle $x^2+y^2=9$ is $x=2$, then area, in square units, of triangle formed by tangents drawn from $P$ to the circle and their chord of contact is equal to

JEE MATHEMATICS MCQ: CIRCLES

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Application +4 | -1

If a chord of contact of tangents drawn from a point

P

with respect to the circle

x^2+y^2=9

x=2

, then area, in square units, of triangle formed by tangents drawn from

P

to the circle and their chord of contact is equal to

View answer and explanation

Correct option: C

\frac{5 \sqrt{5}}{2}

Option C (

\frac{{5 \sqrt 5 }}{{2}}

) is correct because it is the area of the triangle formed by the tangents and chord of contact, calculated using the formula with the given circle and point P.

More Questions from CIRCLES

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The sum of the coefficients in the expansion of

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

as a polynomial in

x

, vanishes. Position of the point

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

with respect to the circle

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

is One of the diameter of the circle

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

is The locus of the middle point of the chords of the circle

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

such that the chords pass through a given point

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

, is

\quad \alpha, \beta

and

\gamma

are the parametric angles of three points

P, Q

, and R respectively, on the circle

x^2+y^2=1

, and

A

is the point

(-1,0)

. If the lengths of the chords

A P, A Q

and

A R

are in

G P

, then

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

and

\cos \gamma / 2

are in The radius of the circle passing through the point (6,2), two of whose diameters are

x+y=6

and

x+2 y=4

is If a circle has two of its diameters along the lines

x+y=5

and

x-y=1

and has area

9 \pi

, then the equation of the circle is