TS EAMCET · Maths · Pair of Lines

A straight line passing through the point $(1, 0)$ and not parallel to $x$ -axis intersects the curve $2 x^{2} + 5 y^{2} - 7 x = 0$ at two points $A$ and $B$ . The angle subtended by the line segment $A B$ at the origin is

A $30 °$
B $45 °$
C $60 °$
D $90 °$

Verified Solution

Answer & Solution

Correct Answer

(D) $90 °$

Step-by-step Solution

Detailed explanation

Let the equation of line is y=mx-1=mx-m Given curve 2x2+5y2-7x=0 ...i Now line mx-ym=1 ...ii Using homogenization 2x2+5y2-7xmx-ym=0 ⇒2mx2+5my2-7mx2+7xy=0 ⇒5my2-5mx2+7xy=0 Here a=-5m, b=5m, h=72 Now, angle tanθ=2h2-aba+b Now,…

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 the point 1, 0 and not parallel to x-axis intersects the curve 2x2+5y2-7x=0 at two points A and B. The angle subtended by the line segment AB at the origin is

Step-by-step Solution

A straight line passing through the point $(1, 0)$ and not parallel to $x$ -axis intersects the curve $2 x^{2} + 5 y^{2} - 7 x = 0$ at two points $A$ and $B$ . The angle subtended by the line segment $A B$ at the origin is