If `p and q` are the intercept on the axis cut by the tangent of `sqrt((x/a))+sqrt((y/b))=1,` prove that `p/a+q/b=1`

The length of intercept on y -axis made by a tangent to (x^(2))/(25)+(y^(2))/(6)=1 with slope sqrt(3) ,is

If p,q varepsilon N satisfy the equation x^(sqrt(x)=(sqrt(x))^(x)) then p&q are

Any tangent to an ellips (x^(2))/(a^(2))+(y^(2))/(b^(2))=1, (a gt b) cut by the tangents at the end points of major axis is T and T' . Prove that the length of intercept of the major axis cut by the circle describe on T T' as diameter is constant and equal to 2sqrt(a^(2)-b^(2)) .

Two circles cut at A and B and a straight line PAQ cuts the circles at P and Q.If the tangents at P and Q intersects at R, prove that R,PB,Q are concyclic.

Let P and Q be two points on the minor axis each at distance sqrt(a^(2)-b^(2))(a>b) from the centre of the ellipse and p and q be the lengths of the perpendiculars upon any tangent from P and Q then find the value of p^(2)+q^(2)

The value of sqrt(p^(-1)q).sqt(q^(-1)r).sqrt(r^(-1) p) is

If the roots of the equation 2x^(2)+7x+4=0 are in the ratio p:q, then the value of sqrt((p)/(q))+sqrt((q)/(p))

Locus of the middle points of the line segment joining P(0, sqrt(1-t^2) + t) and Q(2t, sqrt(1-t^2) - t) cuts an intercept of length a on the line x+y=1 , then a = (A) 1/sqrt(2) (B) sqrt(2) (C) 2 (D) none of these

Consider the curves C_(1):|z-2|=2+Re(z) and C_(2):|z|=3 (where z=x+iy,x,y in R and i=sqrt(-1) .They intersect at P and Q in the first and fourth quadrants respectively.Tangents to C_(1) at P and Q intersect the x- axis at R and tangents to C_(2) at P and Q intersect the x -axis at S .If the area of Delta QRS is lambda sqrt(2) ,then find the value of (lambda)/(2)

If any line perpendicular to the transverse axis cuts the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and the conjugate hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=-1 at points P and Q, respectively,then prove that normal at P and Q meet on the x-axis.