JEE MATHEMATICS MCQ: CIRCLES

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Analyzing +4 | -1

Let

P

and

Q

be any points on the curves

(x-1)^2+

(y+1)^2=1

and

y=x^2

, respectively. The distance between

P

and

Q

is minimum for some value of the abscissa of

P

in the interval

View answer and explanation

Correct option: C

\left(\frac{1}{4}, \frac{1}{2}\right)

Option C

\left(\frac{1}{4}, \frac{1}{2}\right)

is correct because it involves finding the point on the circle closest to the parabola, which requires analyzing the normal to the parabola and its intersection with the circle.

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