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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"))`
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Solution
`(-("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"))`
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