If the two tangents drawn on hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] in such a way that the product of their gradients is \[{{c}^{2}}\], then they intersects on the curve

\[{{y}^{2}}+{{b}^{2}}={{c}^{2}}({{x}^{2}}+{{a}^{2}})\]

\[{{y}^{2}}+{{b}^{2}}={{c}^{2}}({{x}^{2}}-{{a}^{2}})\]

\[{{y}^{2}}+{{b}^{2}}={{c}^{2}}({{x}^{2}}+{{a}^{2}})\]

\[a{{x}^{2}}+b{{y}^{2}}={{c}^{2}}\]

If the two tangents drawn on hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\

1.	If the two tangents drawn on hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] in such a way that the product of their gradients is \[{{c}^{2}}\], then they intersects on the curve
A.	\[{{y}^{2}}+{{b}^{2}}={{c}^{2}}({{x}^{2}}-{{a}^{2}})\]
B.	\[{{y}^{2}}+{{b}^{2}}={{c}^{2}}({{x}^{2}}+{{a}^{2}})\]
C.	\[a{{x}^{2}}+b{{y}^{2}}={{c}^{2}}\]
D.	None of these
Answer» B. \[{{y}^{2}}+{{b}^{2}}={{c}^{2}}({{x}^{2}}+{{a}^{2}})\]

Discussion

No Comment Found

Related MCQs

If the eccentricity of the two ellipse \[\frac{{{x}^{2}}}{169}+\frac{{{y}^{2}}}{25}=1\]and \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] are equal, then the value of \[a/b\] is [UPSEAT 2001]
C the centre of the hyperbola\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\]. The tangents at any point P on this hyperbola meets the straight lines \[bx-ay=0\]and \[bx+ay=0\] in the points Q and R respectively. Then \[CQ\ .\ CR=\]
If the two tangents drawn on hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] in such a way that the product of their gradients is \[{{c}^{2}}\], then they intersects on the curve
Equation \[\frac{1}{r}=\frac{1}{8}+\frac{3}{8}\cos \theta \] represents [EAMCET 2002]
Tangent is drawn to ellipse \[\frac{{{x}^{2}}}{27}+{{y}^{2}}=1\] at \[(3\sqrt{3}\cos \theta ,\ \sin \theta )\] where \[\theta \in (0,\ \pi /2)\]. Then the value of \[\theta \] such that sum of intercepts on axes made by this tangent is minimum, is [IIT Screening 2003]
The area of the quadrilateral formed by the tangents at the end points of latus rectum to the ellipse \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{5}=1\], is [IIT Screening 2003]
The eccentricity of an ellipse, with its centre at the origin, is \[\frac{1}{2}\]. If one of the directrices is \[x=4\], then the equation of the ellipse is [AIEEE 2004]
The co-ordinates of the foci of the ellipse \[3{{x}^{2}}+4{{y}^{2}}-12x-8y+4=0\] are
The equation \[14{{x}^{2}}-4xy+11{{y}^{2}}-44x-58y+71=0\] represents [BIT Ranchi 1986]
The centre of the ellipse \[4{{x}^{2}}+9{{y}^{2}}-16x-54y+61=0\] is [MP PET 1992]

If the two tangents drawn on hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] in such a way that the product of their gradients is \[{{c}^{2}}\], then they intersects on the curve

Discussion

No Comment Found

Related MCQs

Reply to Comment