A) circle of radius 2.
B) parabola of length of latus-rectum 4.
C) ellipse with length of semi-major axis 2.
D) hyperbola with length of semi-transverse axis \[\sqrt{2}\].
Correct Answer: A
Solution :
\[\frac{x}{a}+\frac{y}{b}=1\] ?(1) \[\therefore \] Equation of line is \[hx+ky={{h}^{2}}+{{k}^{2}}\] So, on comparing (1) and (2), we get \[\frac{1}{a}\,=\frac{h}{{{h}^{2}}+{{k}^{2}}}\,;\,\frac{1}{b}\,=\frac{k}{{{h}^{2}}+{{k}^{2}}}\] As, \[\frac{1}{{{a}^{2}}}\,+\frac{1}{{{b}^{2}}}\,=\frac{1}{4}\] \[\Rightarrow \,\,{{h}^{2}}+{{k}^{2}}=4,\] which is circle of radius 2.You need to login to perform this action.
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