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JEE MATHEMATICS MCQ: CIRCLES

1 Easy

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Application +4 | -1

The length of the longest ray drawn from the point

(4,3)

to the circle

x^2+y^2+16 x+18 y+1=0

is equal to

View answer and explanation

Correct option: A

the radius of the circle

Option A (the radius of the circle) is correct because the longest ray from a point to a circle is along the line connecting the point to the center of the circle, extending to the circle's circumference. The length of the tangent is equal to the radius in this case.

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)

\quad \alpha, \beta

\gamma

are the parametric angles of three points

P, Q

, and R respectively, on the circle

x^2+y^2=1

A

(-1,0)

. If the lengths of the chords

A P, A Q

A R

G P

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

\cos \gamma / 2

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

x+y=6

x+2 y=4

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

x+y=5

x-y=1

9 \pi

, then the equation of the circle is