Consider the region R = {(x, y) $$\in$$ R $$\times$$ R : x $$\ge$$ 0 and y2 $$\le$$ 4 $$-$$ x}. Let F be the family of all circles that are contained in R and have centers on the x-axis. Let C be the circle that has largest radius among the circles in F. Let ($$\alpha$$, $$\beta$$) be a point where the circle C meets the curve y2 = 4 $$-$$ x.
$$\Rightarrow$$ $$h = {3 \over 2},h = {{ - 5} \over 2}$$ (Rejected) because part of circle lies outside R. So, $$h = {3 \over 2}$$ = radius of circle (c).
Consider the region R = {(x, y) $$\in$$ R $$\times$$ R : x $$\ge$$ 0 and y2 $$\le$$ 4 $$-$$ x}. Let F be the family of all circles that are contained in R and have centers on the x-axis. Let C be the circle that has largest radius among the circles in F. Let ($$\alpha$$, $$\beta$$) be a point where the circle C meets the curve y2 = 4 $$-$$ x.
$$\Rightarrow$$ $$h = {3 \over 2},h = {{ - 5} \over 2}$$ (Rejected) because part of circle lies outside R. So, $$h = {3 \over 2}$$ = radius of circle (C).
3
JEE Advanced 2020 Paper 2 Offline
Numerical
Let O be the centre of the circle x2 + y2 = r2, where $$r > {{\sqrt 5 } \over 2}$$. Suppose PQ is a chord of this circle and the equation of the line passing through P and Q is 2x + 4y = 5. If the centre of the circumcircle of the triangle OPQ lies on the line x + 2y = 4, then the value of r is .............
Your Input ________
Answer
Correct Answer is 2
Explanation
As we know that the equation of family of circles passes through the points of intersection of given circle x2 + y2 = r2 and line PQ : 2x + 4y = 5 is,
Let the point B be the reflection of the point A(2, 3) with respect to the line $$8x - 6y - 23 = 0$$. Let $$\Gamma_{A} $$ and $$\Gamma_{B} $$ be circles of radii 2 and 1 with centres A and B respectively. Let T be a common tangent to the circles $$\Gamma_{A} $$ and $$\Gamma_{B} $$ such that both the circles are on the same side of T. If C is the point of intersection of T and the line passing through A and B, then the length of the line segment AC is .................
Your Input ________
Answer
Correct Answer is 10
Explanation
According to given information the figure is as following