The chord `P Q` of the rectangular hyperbola `x y=a^2` meets the axis of `x` at `A ; C` is the midpoint of `P Q ;` and `O` is the origin. Then ` A C O` is (a) equilateral (b) isosceles (c) right-angled (d) right isosceles

Ifthe normal at P to the rectangular hyperbola x^2-y^2=4 meets the axes in G and g and C is the centre of the hyperbola, then

If P N is the perpendicular from a point on a rectangular hyperbola x y=c^2 to its asymptotes, then find the locus of the midpoint of P N

The normal to a curve at P(x , y) meet the x-axis at Gdot If the distance of G from the origin is twice the abscissa of P , then the curve is a (a) parabola (b) circle (c) hyperbola (d) ellipse

If all the vertices of a triangle have integral coordinates, then the triangle may be (a) right-angle (b) equilateral (c) isosceles (d) none of these

If a vertex, the circumcenter, and the centroid of a triangle are (0, 0), (3,4), and (6, 8), respectively, then the triangle must be (a) a right-angled triangle (b) an equilateral triangle (c) an isosceles triangle (d) a right-angled isosceles triangle

If the tangent at the point P(2,4) to the parabola y^2=8x meets the parabola y^2=8x+5 at Qa n dR , then find the midpoint of chord Q Rdot

In a triangle A B C , the altitude from A is not less than B C and the altitude from B is not less than A C . (a)The triangle is right angled (b) isosceles obtuse angled (d) equilateral

If tangents O Q and O R are dawn to variable circles having radius r and the center lying on the rectangular hyperbola x y=1 , then the locus of the circumcenter of triangle O Q R is (O being the origin). (a) x y=4 (b) x y=1/4 x y=1 (d) none of these

ABC is an isosceles triangle right angled at C. Prove that AB^(2) = 2AC^(2) .

P Q and R S are two perpendicular chords of the rectangular hyperbola x y=c^2dot If C is the center of the rectangular hyperbola, then find the value of product of the slopes of C P ,C Q ,C R , and C Sdot