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CBSE Class 11-commerce Answered

Find equation of parabola whose vertex is (2,-3)and focus is (0,5)
Asked by deepakagarwal1024 | 24 Dec, 2018, 09:43: AM
answered-by-expert Expert Answer
Vertex of parabola V(2,-3) and focus F(0,5)
Let the line joining V and F meets the directrix at D(xd , yd)
 
since Vertex is middle point between D and Focus F, we have, (xd+0)/2 = 2 or xd = 4  and (yd + 5)/2 = -3, or yd = -11
 
Hence coordinates of D = (4, -11)
 
slope of line joining focus F and D is given by, begin mathsize 12px style fraction numerator negative 11 minus 5 over denominator 4 minus 0 end fraction space equals space minus 4 end style ; hence slope of directrix = 1/4
equation of directrix = begin mathsize 12px style fraction numerator y plus 11 over denominator x minus 4 end fraction space equals space 1 fourth space o r space x minus 4 y minus 48 space equals space 0 end style
let a point P(x , y) is on parabola.
distance between focus S and P i.e. SP is equal to the perpendicular distance from P to Directrix.
 
hence begin mathsize 12px style square root of x squared plus open parentheses y minus 5 close parentheses squared end root space equals space fraction numerator x minus 4 y minus 48 over denominator square root of 17 end fraction space space o r space space space 17 open square brackets x squared plus open parentheses y minus 5 close parentheses squared close square brackets space equals space open parentheses x minus 4 y minus 48 close parentheses squared end style..................(1)
Above eqn.(1) is the equation of parabola whose vertex is (2,-3) and focus is (0,5)
Answered by Thiyagarajan K | 27 Dec, 2018, 10:16: AM

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