TS EAMCET · Maths · Straight Lines

A straight line passing through a fixed point $(3, 5)$ intersects the coordinate axes at two points $A$ and $B .$ If the locus of $C (x, y)$ which forms a rectangle with the points $A, O$ (origin) and $B$ is $a x + 2 h x y + b y = 0$ then $a + b + h =$

A $\frac{17}{2}$
B $7$
C $\frac{15}{2}$
D $10$

Verified Solution

Answer & Solution

Correct Answer

(C) $\frac{15}{2}$

Step-by-step Solution

Detailed explanation

A Straight line passing through a fixed point 3,5 and intersects coordinate axis at point A and B. Let coordinates of Ap,0 and B0,q ∴ Intercept form of line is xp+yq=1 Here, point 3,5 will satisfy the line. ⇒ 3p+5q=1 Here, coordinate of point are…

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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A straight line passing through a fixed point 3, 5 intersects the coordinate axes at two points A and B. If the locus of Cx, y which forms a rectangle with the points A, O (origin) and B is ax+2hxy+by=0 then a+b+h=

Step-by-step Solution

A straight line passing through a fixed point $(3, 5)$ intersects the coordinate axes at two points $A$ and $B .$ If the locus of $C (x, y)$ which forms a rectangle with the points $A, O$ (origin) and $B$ is $a x + 2 h x y + b y = 0$ then $a + b + h =$