Calculate the points on an ellipse that have tangents that pass through a point

[41193jms]

Homework Statement

Find the points on the ellipse x^2/100 + y^2/49 = 1 that have tangents that pass through the point P(2, 7.7)

Homework Equations

The Attempt at a Solution

I calculated the gradient of the ellipse which came to dy/dx = -49x/100y
I then calculated the gradient of the tangent that passes through the point P(x,y) on the ellipse as dy/dx = 7.7-y/2-x
I then attempted to make these two equations equal to each other -49x/100y = 7.7-y/2-x and use the equation of the ellipse ie. rearrange for x and substitute but it doesn't seem to be getting anywhere

 

[NakedNoodles]

Try substituting into the line equation formula, as opposed to the generic tangent and normal equations engineered for eclipses.

 

[41193jms]

so by using y-y1=m(x-x1) where m is -49x/100y and y1 is 7.7 and x1 is 2
i get y-7.7=-49x/100y(x-2)
when rearranged that becomes 100y^2-770y=-49x^2+98x i don't think that would help

 

[D H]

You just haven't gone far enough. What is y^2?

 

[41193jms]

y^2 by rearranging the ellipse formula is 49(100-x^2)/100 when i attempt to substitute into 100y^2 - 770y = -49x^2 +98x i am still left with a y

 

[D H]

So keep going. Use that if a=b then a^2=b^2.

 

[41193jms]

thanks i got it