Question

Choose the correct alternative.

If ax² + 2hxy + by² = 0 then `"dy"/"dx" = ?` 

Options

• `(("ax" + "hx"))/(("hx" + "by"))`

• `(-("ax" + "hx"))/(("hx" + "by"))`

• `(("ax" - "hx"))/(("hx" + "by"))`

• `(("2ax" + "hy"))/(("hx" + "3by"))`

Answer 1

`(-("ax" + "hx"))/(("hx" + "by"))`

Explanation:

ax² + 2hxy + by² = 0

Differentiating both sides w.r.t.x, we get

`"a"(2"x") + "2h" * "d"/"dx" ("xy") + "b"("2y") "dy"/"dx" = 0`

∴ 2ax + 2h `["x" * "dy"/"dx" + "y"(1)] + 2"by" "dy"/"dx" = 0`

∴ 2ax + 2hx `"dy"/"dx"` + 2hy + 2by`"dy"/"dx"` = 0

∴ 2`"dy"/"dx"`(hx + by) = - 2ax - 2hy

∴ 2`"dy"/"dx" = (-2("ax" + "hy"))/(("hx" + "by"))`

∴ `"dy"/"dx" = (-("ax" + "hx"))/(("hx" + "by"))`