Tangent of acute angle between the curves `y=|x^2-1|` and `y=sqrt(7-x^2)` at their points of intersection is (a) `(5sqrt(3))/2` (b) `(3sqrt(5))/2` `(5sqrt(3))/4` (d) `(3sqrt(5))/4`

A curve is represented by the equations x=sec^2ta n dy=cott , where t is a parameter. If the tangent at the point P on the curve where t=pi/4 meets the curve again at the point Q , then |P Q| is equal to (5sqrt(3))/2 (b) (5sqrt(5))/2 (c) (2sqrt(5))/3 (d) (3sqrt(5))/2

Find the angle between the lines y-sqrt3 x - 5 = 0 and sqrt3 y -x + 6 = 0

The angle between the lines joining the origin to the points of intersection of the line sqrt3x+y=2 and the curve y^(2)-x^(2)=4 is

The points on the line x=2 from which the tangents drawn to the circle x^2+y^2=16 are at right angles is (are) (a) (2,2sqrt(7)) (b) (2,2sqrt(5)) (c) (2,-2sqrt(7)) (d) (2,-2sqrt(5))

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)

In a A B C , if tanA:tanB :tanC=3:4:5, then the value of sinA sinB sinC is equal to (a) 2/(sqrt(5)) (b) (2sqrt(5))/7 (2sqrt(5))/9 (d) 2/(3sqrt(5))

Find the acute angle between the pair of straight lines whose direction cosines are sqrt(3)/4, -1/4, -sqrt(3)/2 and -sqrt(3)/4, 1/4, -sqrt(3)/2

Show that 4sin27^0=(5+sqrt(5))^(1/2)+(3-sqrt(5))^(1/2)

The ellipse 4x^2+9y^2=36 and the hyperbola a^2x^2-y^2=4 intersect at right angles. Then the equation of the circle through the points of intersection of two conics is (a) x^2+y^2=5 (b) sqrt(5)(x^2+y^2)-3x-4y=0 (c) sqrt(5)(x^2+y^2)+3x+4y=0 (d) x^2+y^2=25

Simplify : (sqrt5+sqrt3)((3sqrt3)/(sqrt5+sqrt2)-sqrt5/(sqrt3+sqrt2))