Analytic geometry

[Mel Mitch]

Hello everyone, i have two questions that i'm not sure how to find the answer could anyone explain to me. but it must be sloved analytically

(1)Find the equation of the elipses centered at the point (0,7), a vertex at the orgin and (2,3) on the curve.

that is in the form (x-h)/a^2 + (y-K)/b^2=1..... then h=0 and k=7
How do i find for a and b???


(2) the equation of the tangent to the ellipses 16x^2+25y^2=400, through the point (3,4)

hence x^2/25+y^2/16=1......now i'm puzzled what step to take

????Mel

 

[stapel]

(1)Find the equation of the elipses centered at the point (0,7), a vertex at the orgin and (2,3) on the curve.

You are given that (h, k) = (0, 7), and that one vertex is at (0, 0). This tells you that a = 7, and that a^2 goes with the x-squared term. You are given that (x, y) = (2, 3) is on the ellipise. Putting this together, you have:

. . . . .\(\displaystyle \frac{2^2}{49}\, +\, \frac{(3\, -\, 7)^2}{b^2}\, =\, 1\)

Solve for the value of b.

Gotta run.... :wink:

 

[Mel Mitch]

thanks staples........i was able to continue..........