Let any double ordinate `P N P '`
of the hyperbola `(x^2)/(25)-(y^2)/(16)=1`
be produced on both sides to meet the asymptotes in `Qa n dQ '`
. Then `P QdotP^(prime)Q`
is equal to
25 (b) 16 (c) 41
(d) none of these
The tangent at P on the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2))=1 meets one of the asymptote in Q. Then the locus of the mid-point of PQ is
The circle x^2+y^2=5 meets the parabola y^2=4x at P and Q . Then the length P Q is equal to (A) 2 (B) 2sqrt(2) (C) 4 (D) none of these
A normal to the hyperbola (x^2)/4-(y^2)/1=1 has equal intercepts on the positive x- and y-axis. If this normal touches the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 , then a^2+b^2 is equal to (a)5 (b) 25 (c) 16 (d) none of these
If the normals to the parabola y^2=4a x at three points P ,Q ,a n dR meet at A ,a n dS is the focus, then S PdotS qdotS R is equal to a^2S A (b) S A^3 (c) a S A^2 (d) none of these
If P Q is a double ordinate of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 such that O P Q is an equilateral triangle, O being the center of the hyperbola, then find the range of the eccentricity e of the hyperbola.
The ellipse (x^(2))/(25)+(y^(2))/(16)=1 and the hyperbola (x^(2))/(25)-(y^(2))/(16) =1 have in common
Let d_1a n dd_2 be the length of the perpendiculars drawn from the foci Sa n dS ' of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 to the tangent at any point P on the ellipse. Then, S P : S^(prime)P= (a) d_1: d_2 (b) d_2: d_1 (c) d_1 ^2:d_2 ^2 (d) sqrt(d_1):sqrt(d_2)
P N is the ordinate of any point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 and AA ' is its transvers axis. If Q divides A P in the ratio a^2: b^2, then prove that N Q is perpendicular to A^(prime)Pdot
If p >1 and q >1 are such that log(p+q)=logp+logq , then the value of log(p-1)+log(q-1) is equal to (a) 0 (b) 1 (c) 2 (d) none of these
P is a point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,N is the foot of the perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transvers axis at Tdot If O is the center of the hyperbola, then find the value of O TxO Ndot
