TS EAMCET · Maths · Straight Lines

If the perimeter of a triangle is $20$ and two of its vertices are $(- 5, 0)$ and $(6, 0)$ , then the locus of the third vertex is
tions:

A $40 x^{2} - 81 y^{2} - 40 x - 800 = 0$
B $40 x^{2} + 9 y^{2} - 25 x + 800 = 0$
C $40 x^{2} - 9 y^{2} = 800$
D $5 x^{2} - 3 y^{2} + 3 x - 4 y + 25 = 0$

Verified Solution

Answer & Solution

Correct Answer

(A) $40 x^{2} - 81 y^{2} - 40 x - 800 = 0$

Step-by-step Solution

Detailed explanation

Given, The perimeter of a triangle is 20 and two of its vertices are -5,0 and 6,0, Now let the third vertex be x,y, Now by formula of perimeter of triangle we get, 20=x+52+y2+6+52+x-62+y2 ⇒20=x+52+y2+11+x-62+y2 ⇒9-x-62+y2=x+52+y2 Now squaring both side we get,…

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.

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If the perimeter of a triangle is 20 and two of its vertices are -5,0 and 6,0, then the locus of the third vertex istions:

Step-by-step Solution

If the perimeter of a triangle is $20$ and two of its vertices are $(- 5, 0)$ and $(6, 0)$ , then the locus of the third vertex is
tions: