A) an ellipse
B) a circle
C) a parabola
D) a hyperbola
Correct Answer: D
Solution :
Line\[y=mx+c\]will be a tangent to hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1.\]If \[{{c}^{2}}={{a}^{2}}{{m}^{2}}-{{b}^{2}}\] Similarly, line\[y=ax+\beta \] will be tangent, if \[{{\beta }^{2}}={{\alpha }^{2}}{{a}^{2}}-{{b}^{2}}\] \[\therefore \] Locus of\[(\alpha ,\beta )\]is \[{{y}^{2}}={{a}^{2}}{{x}^{2}}-{{b}^{2}}\] \[\Rightarrow \] \[{{a}^{2}}{{x}^{2}}-{{y}^{2}}-{{b}^{2}}=0\] Since, this equation represent a hyperbola. \[\therefore \] Locus of\[P(\alpha ,\beta )\]is a hyperbola.
You need to login to perform this action.
You will be redirected in
3 sec
