ELLIPSE: 4x^2+9y^2=36 is equation of a ellipse  Find the equation of the line from the origin to the point x=d (the radial). where x is the first quadrant     

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to write the standard form of ellipse, hence, you need to divide the equation by 36 such that:

`x^2/9 + y^2/4 = 1`

Hence, the semi-major axis is `a=3`  and the semi-minor axis is `b=2` .

You should know that the radial line from origin to the point (a,b) intercepts the ellipse at `(a/sqrt2,b/sqrt2).`

Hence, evaluating the coordinates of point of intersection yields `(3/sqrt2,2/sqrt2).`

You need to write the equation of the radial line such that:

`y - 0 = (2/sqrt2)/(3/sqrt2)(x - 0)`

`y = (2/3)x`

Hence, evaluating the equation of the radial line under given conditions yields `y = (2/3)x` .

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