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JEE MATHEMATICS MCQ: CIRCLES

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Equation of the smaller circle that touches the circle x2+y2=1x^2+y^2=1 and passes through the point (4,3)(4,3), is
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Correct option: A
5(x2+y2)βˆ’24xβˆ’18y+25=05\left(x^2+y^2\right)-24 x-18 y+25=0
Option A (5(x2+y2)βˆ’24xβˆ’18y+25=05(x^2+y^2)-24x-18y+25=0) is correct because it represents a circle that touches the given circle and passes through the given point.

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The sum of the coefficients in the expansion of (Ξ±2x2βˆ’2Ξ±x+1)51,{\left( {{\alpha ^2}{x^2} - 2\alpha \mathrm{ }x + 1} \right)^{51}}, as a polynomial in xx, vanishes. Position of the point (Ξ±,2Ξ±2)\left( {\alpha ,2{\alpha ^2}} \right) with respect to the circle x2+y2=4,{x^2} + {y^2} = 4, is One of the diameter of the circle x2+y2βˆ’2x+4yβˆ’4=0{x^2} + {y^2} - 2x + 4y - 4 = 0 is The locus of the middle point of the chords of the circle x2+y2=a2{x^2} + {y^2} = {a^2} such that the chords pass through a given point (x1,y1)\left( {{x_1},{y_1}} \right), is Ξ±,Ξ²\quad \alpha, \beta and Ξ³\gamma are the parametric angles of three points P,QP, Q, and R respectively, on the circle x2+y2=1x^2+y^2=1, and AA is the point (βˆ’1,0)(-1,0). If the lengths of the chords AP,AQA P, A Q and ARA R are in GPG P, then cos⁑α/2,cos⁑β/2\cos \alpha / 2, \cos \beta / 2 and cos⁑γ/2\cos \gamma / 2 are in The radius of the circle passing through the point (6,2), two of whose diameters are x+y=6x+y=6 and x+2y=4x+2 y=4 is If a circle has two of its diameters along the lines x+y=5x+y=5 and xβˆ’y=1x-y=1 and has area 9Ο€9 \pi, then the equation of the circle is
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