The point P on the ellipse `4x^2+9y^2=36` is such that the are of the ` P F_1F_2=sqrt(10)` where `F_1,f_2` are foci. Then P has the coordinates `(3/(sqrt(2)),sqrt(2))` (b) `(3/2,2)` `(-3/2,-2)` (d) `(-3/(sqrt(2))-sqrt(2))`

The point,at shortest distance from the line x+y=10 and lying on the ellipse x^(2)+2y^(2)=6, has coordinates (A) (sqrt(2),sqrt(2)) (B) (0,sqrt(3))(C)(2,1)(D)(sqrt(5),(1)/(sqrt(2)))

(1)/(sqrt(9)-sqrt(8)) is equal to: 3+2sqrt(2)(b)(1)/(3+2sqrt(2)) (c) 3-2sqrt(2)(d)(3)/(2)-sqrt(2)

If P and Q are two points on the circle x^2 + y^2 - 4x + 6y-3=0 which are farthest and nearest respectively from the point (7, 2) then. (A) P-=(2-2sqrt(2), -3-2sqrt(2)) (B) Q-= (2+2sqrt(2), -3 + 2 sqrt(2)) (C) P-= (2+2sqrt(2), -3 + 2 sqrt(2)) (D) Q-= (2-2sqrt(2), -3 + 2 sqrt(2))

If x=5+2sqrt(6), then sqrt(x)-(1)/(sqrt(x)) is a.2sqrt(2)b2sqrt(3)c*sqrt(3)+sqrt(2)d*sqrt(3)-sqrt(2)

(iv) Prove that the domain of f(x)=sqrt(9-x^(2))+sqrt(x^(2)-4) is [-3,2]U[2,3l

A circle C of radius 1 is inscribed in an equilateral triangle PQR . The points of contact of C with the sides PQ, QR, RP and D, E, F respectively. The line PQ is given by the equation sqrt(3) +y-6=0 and the point D is ((sqrt(3))/(2), 3/2) . Point E and F are given by : (A) (sqrt(3)/2, 3/2), (sqrt(3), 0) (B) (sqrt(3)/2, 3/2), (sqrt(3)/2, 1/2) (C) (3/2, sqrt(3)/2), (sqrt(3)/2, 1/2)

P is any variable point on the ellipse 4x^(2) + 9y^(2) = 36 and F_(1), F_(2) are its foci. Maxium area of trianglePF_(1)F_(2) ( e is eccentricity of ellipse )

" (vii) f(x)=3x^(2)-1;x=(1)/(sqrt(3)),(2)/(sqrt(3))

The normal at a point P on the ellipse x^2+4y^2=16 meets the x-axis at Qdot If M is the midpoint of the line segment P Q , then the locus of M intersects the latus rectums of the given ellipse at points. (a)(+-((3sqrt(5)))/2+-2/7) (b) (+-((3sqrt(5)))/2+-(sqrt(19))/7) (c)(+-2sqrt(3),+-1/7) (d) (+-2sqrt(3)+-(4sqrt(3))/7)

The direction ratio o the lien OP are euqla and the length OP=sqrt(3) . Then the cooredinates of the point P are (A) (-1,-1,-1) (B) (sqrt(3),sqrt(3),sqrt(3)) (C) (sqrt(2),sqrt(2),sqrt(2)) (D) (2,2,2)