JEE MATHEMATICS MCQ: CIRCLES

1 Easy

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Analyzing +4 | -1

Let the circle

S:36{x^2} + 36{y^2} - 108x + 120y + C = 0

be such that it neither intersects nor touches the coordinate axes. If the point of intersection of the lines

x - 2y = 4

and

2x - y = 5

lies inside the circle

S

, then

View answer and explanation

Correct option: D

100\, < \,C\, < \,156

Option D (

100 < C < 156

) is correct because the circle must neither intersect nor touch the coordinate axes, and the point of intersection of the lines must lie inside the circle, leading to the specified range for C.

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