book Maths Puzzle Numerical Ability

Find the equation of the ellipse whose center is (5,-3)that has a vertex at (13,-3) and a minor axis of length 10.

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book Other Question
What is the equation of conic sections and how do you get the formula? How would you solve the following problems:

3(-2-3x)=-9x-4
5/2t-t=3/2t+3