JAMB 1989 · UME · Q22

Quadratics & their graphs

What are $K$ and $L$ respectively if $\frac12(3y - 4x)^2 = 8x^2 + Kxy + Ly^2$ ?

Worked solution (try it first)

Expand the bracket: $(3y - 4x)^2 = 9y^2 - 24xy + 16x^2$ .
Halve every term: $\frac12(3y - 4x)^2 = 8x^2 - 12xy + \frac92y^2$ .
Compare with $8x^2 + Kxy + Ly^2$ : $K = -12$ and $L = \frac92$ , option A.

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