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If x2 + 3xy + 2y2 - x - 4y - 6 = 0 represents a pair of straight lines, their point if intersection is
1. (0, 0)
2. (8, 5)
3. (8, -5)
4. (-2, 5)

1 Answer

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Best answer
Correct Answer - Option 3 : (8, -5)

Concept:

partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant.

Example: partial differentiate w.r.t. x then y will be constant and vice versa.(for function containing x and y variables).

 

Calculation:

Let, ϕ (x, y) = x2 + 3xy + 2y2 - x - 4y - 6 = 0

Taking partial derivative w.r.t. x, we get 

\(\rm \frac{dϕ }{dx}=2x+3y-1=0\cdots (1)\)

Taking partial derivative w.r.t. x, we get 

\(\rm \frac{dϕ }{dy}=3x+4y-4=0\cdots (2)\)

Multiplying (1) by 3 and (2) by 2, we get 

\(\rm 6x+9y-3=0\cdots (3)\) and \(\rm 6x+8y-8=0\cdots (4)\)

Now , subtracting (4) from (3), we get 

y + 5 = 0 ⇒ y = -5

From (1), 2x + 3(-5) -1 = 0

⇒ x = 8

So, the point of intersection is (8, -5)

Hence, option (3) is correct.

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