Let `E` be the ellipse `(x^2)/9+(y^2)/4=1` and `C` be the circle `x^2+y^2=9` . Let `Pa n dQ` be the points (1, 2) and (2, 1), respectively. Then, (a) `Q` lies inside `C` but outside `E` (b) `Q` lies outside both `Ca n dE` (c) `P` lies inside both `C` and `E` (d) `P` lies inside `C` but outside `E`

Does the point (–2.5, 3.5) lie inside, outside or on the circle x^2 + y^2 = 25 ?

The centroid of the triangle formed by the points (1,a), (2,b) and (c^2,-3) by which condition the points lies on the x-axis

The point (8,4) lies inside the parabola y^(2) = 4ax If _

Normal to the ellipse (x^2)/(64)+(y^2)/(49)=1 intersects the major and minor axes at Pa n dQ , respectively. Find the locus of the point dividing segment P Q in the ratio 2:1.

Let C_1 and C_2 be two circles whose equations are x^2+y^2-2x=0 and x^2+y^2+2x=0 and P(lambda, lambda) is a variable point . List 1 a) P lies inside C_1 ​ but outside C_2 ​ b)P lies inside C_2 ​ but outside C_1 ​ c)P lies outside C_1 ​ but outside C_2 ​ d)P does not lie inside C_2 ​ List 2 p)λ ϵ (−∞,−1)∪(0,∞) q)λ ϵ (−∞,−1)∪(1,∞) r)λ ϵ (−1,0) s)λ ϵ (0,1)

Let C_(1) and C_(2) denote the centres of the circles x^(2) +y^(2) = 4 and (x -2)^(2) + y^(2) = 1 respectively and let P and Q be their points of intersection. Then the areas of triangles C_(1) PQ and C_(2) PQ are in the ratio _

If each of the points (x_1, 4), (-2,y_1) lies on the line joining the points (2, -1), (5, -3), then the points P(x_1, y_1) lies on the line :

If the point (2a,a) lies inside the parabola x^(2) -2x - 4y +3 = 0 , then a lies in the interval

Consider the circles x^2+(y-1)^2=9,(x-1)^2+y^2=25. They are such that a.these circles touch each other b.one of these circles lies entirely inside the other c.each of these circles lies outside the other d.they intersect at two points.