find the points of tangency

Question

Find the points of tangency given f(x) = 15/2/x is tangent to x²/25 + y²/9 = 1

Answer 1

that's the equation of an ellipse, with center at the origin

f(x) = 15/2/x is probably a mistake or typo of some kind.

does it mean y= (15/2)x? IF so, there is no point where it's tangent to the ellipse. It intersects the ellipse in 2 points though and goes through the center of the ellipse at the origin.

Maybe you meant y=15/2x? That's a hyperbola which graphically in a rough sketch does look like it may be tangent to the ellipse in 2 points, one in Quadrant I at about (3.4,2.2) and in Quadrant III at (-3.4,-2.2)