AP EAMCET · Maths · Pair of Lines

If the lines, joining the origin to the points of intersection of the curve $2 x^{2} - 2 x y + 3 y^{2} + 2 x - y - 1 = 0$ and the line $x + 2 y = k$ , are at right angles, then $k^{2}$ equals

A $4$
B $3$
C $2$
D $1$

Verified Solution

Answer & Solution

Correct Answer

(D) $1$

Step-by-step Solution

Detailed explanation

Equation of line x+2y=k Also x+2yk=1 …1 2x2-2xy+3y2+2x-y-1=0 …2 Homogenise equation 2 with respect to 1 2x2-2xy+3y2+2x-y1-112=0 2x2-2xy+3y2+2x-yx+2yk-1x+2yk2=0 2x2-2xy+3y2k2+2x-yx+2yk-x2+4y2+4xy=0 x22k2+2k-1+xy-2k2+3k-4+y23k2-2k-4=0 Given these…

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

If the lines, joining the origin to the points of intersection of the curve 2x2-2xy+3y2+2x-y-1=0 and the line x+2 y=k, are at right angles, then k2 equals

Step-by-step Solution

If the lines, joining the origin to the points of intersection of the curve $2 x^{2} - 2 x y + 3 y^{2} + 2 x - y - 1 = 0$ and the line $x + 2 y = k$ , are at right angles, then $k^{2}$ equals