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CBSE Class 11-science Answered

8. If one axis of  a  varying central conic ( hyperbola ) is fixed in magnitude and position, prove that the locus of the point of contact of a  tangent drawn to it from a fixed point on the other axis is a parabola.
Asked by sudhanshubhushanroy | 31 Mar, 2018, 10:41: AM
answered-by-expert Expert Answer
begin mathsize 16px style tangent space parametric space at space left parenthesis straight h comma straight k right parenthesis........ space space straight h equals straight a space sec space straight theta comma space space straight k equals straight b space tan space straight theta fraction numerator straight x space secθ over denominator straight a end fraction minus fraction numerator straight y space tan space straight theta over denominator straight b end fraction equals 1 now space straight a space point space on space axis space lies space on space it space left parenthesis straight c comma 0 right parenthesis space sub minus straight c space tan space straight theta space equals space straight b sub space value space of space straight b space in space straight k straight k over straight c equals negative tan squared straight theta space and space straight h over straight a equals sec space straight theta...... sq.... open parentheses straight h over straight a close parentheses squared equals sec squared space straight theta use space sec squared space straight theta minus tan squared straight theta equals 1 end style
Answered by Arun | 02 Apr, 2018, 11:44: AM

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CBSE 11-science - Maths
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