JEE MATHEMATICS MCQ: CIRCLES

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Analyzing +4 | -1

Choose the incorrect statement about the two circles whose equations are given below

{x^2} + {y^2} - 10x - 10y\mathrm{ } + 41\mathrm{ } = \mathrm{ }0

and

{x^2} + {y^2} - \mathrm{ }16x\mathrm{ }-\mathrm{ }10y\mathrm{ } + \mathrm{ }80\mathrm{ } = \mathrm{ }0

View answer and explanation

Correct option: B

Both circles centres lie inside region of one another

Option B (Both circles centres lie inside region of one another) is the incorrect statement because the centers of each circle lie on the circumference of the other, not inside.

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