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  • Find the equation to the parabola whose axis parallel to the y axis and which passes through the point (0,4) (1,9) and (4,5) and determine its latus rectum

Find the equation to the parabola whose axis parallel to the y axis and which passes through the point (0,4) (1,9) and (4,5) and determine its latus rectum

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Solution: The equation of the parabola parallel to y axis is

y=Ax^2+Bx+C ...........(1)

The point (0,4)(1,9);and;(4,5) lie on (1) then

4=0+0+CRightarrow C=4.......(2)\ \Rightarrow 9=A+B+CRightarrow A+B=5......(3)\ \Rightarrow 5=16A+4B+CRightarrow 4A+B=1/4......(4)\ \Rightarrow From;(3);and;(4)\ \Rightarrow A=-19/12;B=79/12

Hence the Equation of parabola

y=(-19/12)x^2+(79/12)x+4

Length of latus rectum =1/left | -19/12 ight |=12/19

Posted by

Deependra Verma

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