The curve represented by the equation `sqrt(p x)+sqrt(q y)=1` where `p ,q in R ,p ,q >0,` is a circle (b) a parabola an ellipse (d) a hyperbola

Consider a curve ax^2+2hxy+by^2=1 and a point P not on the curve. A line drawn from the point P intersect the curve at points Q and R. If he product PQ.PR is (A) a pair of straight line (B) a circle (C) a parabola (D) an ellipse or hyperbola

The roots of the eqaution (q-r)x^(2)+(r-p)x+(p-q)=0 are

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

The locus of the orthocentre of the triangle formed by the lines (1+p) x-py + p(1 + p) = 0, (1 + q)x-qy + q(1 +q) = 0 and y = 0, where p!=*q , is (A) a hyperbola (B) a parabola (C) an ellipse (D) a straight line

P(x , y) is a variable point on the parabola y^2=4a x and Q(x+c ,y+c) is another variable point, where c is a constant. The locus of the midpoint of P Q is an (a)parabola (b) ellipse (c)hyperbola (d) circle

If the roots of the equation (q-r)x^(2)+(r-p)x+p-q=0 are equal, then show that p, q and r are in A.P.

Consider the family of all circles whose centers lie on the straight line y=x . If this family of circles is represented by the differential equation P y^(primeprime)+Q y^(prime)+1=0, where P ,Q are functions of x , y and y^(prime)(h e r ey^(prime)=(dy)/(dx),y^=(d^2y)/(dx^2)), then which of the following statements is (are) true? (a) P=y+x (b) P=y-x (c) P+Q=1-x+y+y^(prime)+(y^(prime))^2 (d) P-Q=x+y-y^(prime)-(y^(prime))^2

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 p , q in N satisfy the equation x^sqrt(x)=(sqrt(x))^x, then pa n dq are (a)relatively prime (b) twin prime (c) coprime (d)if (log)_q p is defined, then (log)_p q is not and vice versa