AP EAMCET · Maths · Pair of Lines

The equation of the pair of straight lines perpendicular to the pair $2 x^{2} + 3 x y + 2 y^{2} + 10 x +$ $5 y = 0$ and passing though the origin is______

A $2 x^{2} + 5 x y + 2 y^{2} = 0$
B $2 x^{2} - 3 x y + 2 y^{2} = 0$
C $2 x^{2} + 3 x y + y^{2} = 0$
D $2 x^{2} - 5 x y + 2 y^{2} = 0$

Verified Solution

Answer & Solution

Correct Answer

(B) $2 x^{2} - 3 x y + 2 y^{2} = 0$

Step-by-step Solution

Detailed explanation

Given equation of Pair of straight lines 2x2+3xy+2y2+10x+5y=0 It is in the form of ax2+2hxy+by2+2gx+2fy+c=0 Here a =2, h = 32, b = 2. Equation perpendicular to given Pair of straight lines passing through origin is bx2-2hxy+ay2=0…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From AP EAMCET

Explore more questions on app

The equation of the pair of straight lines perpendicular to the pair 2x2+3xy+2y2+10x+5y=0 and passing though the origin is______

Step-by-step Solution

The equation of the pair of straight lines perpendicular to the pair $2 x^{2} + 3 x y + 2 y^{2} + 10 x +$ $5 y = 0$ and passing though the origin is______