CircleHardBloom L3
Question
The centre of the smallest circle touching the circles $x^{2} + y^{2} - 2y - 3 = 0$ and $x^{2} + y^{2} - 8x - 18y + 93 = 0$ is:
Options
A.$(3,2)$
B.$(4,4)$
C.$(2,7)$
D.$(2,5)$
Solution
[Key Concept: The smallest circle touching two given circles lies on their line of centres.]
Centre will be mid-point of $C_{1}$ and $C_{2}$
$$\equiv \left( \frac{0 + 4}{2},\frac{1 + 9}{2} \right) = (2,5)$$
Create a free account to view solution
View Solution FreeMore Circle Questions
Let the tangents drawn to the circle, x2 + y2 = 16 from the point P(0, h) meet the x-axis at points A and B. If the area...If (a cos θi, a sin θi)i = 1, 2, 3 represent the vertices of an equilateral triangle inscribed in a circle, th...The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line4x - 5y = 20 ...The intercepts made by the circle x2 + y2 _ 5x _ 13y _ 14 = 0 on the x-axis and y-axis are respectively...If circles x2 + y2 = r2 and x2 + y2 − 20x + 36 = 0 intersect at real and different points, then-...