AP EAMCET · Maths · Circle

If the chord of contact of tangents from a point \(A\) to a given circle passes through \(B\), then the circle with \(A B\) as a diameter will ____

A Touch the given circle internally
B Cut the given circle orthogonally
C Touch the given circle externally
D Neither intersect nor touch the given circle

Verified Solution

Answer & Solution

Correct Answer

(B) Cut the given circle orthogonally

Step-by-step Solution

Detailed explanation

Let an equation of circle \(x^2+y^2+2 g x+2 f y+c=0 \text { and point } A\left(x_1, y_1\right)\) Then equation of chord of contact is…

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

If \(\cos \alpha+\cos \beta=a\) and \(\sin \alpha+\sin \beta=b\), then match the items given in List \(-A\) with those of their values in List-B

List-A	Liat-B
(I) \(\tan \left(\frac{\alpha+\beta}{2}\right)=\)	(a) \(\frac{ b }{ a }\)
(II) \(\cos (\alpha+\beta)=\)	(b) \(\frac{2 a b}{a^2+b^2}\)
(III) \(\sin (\alpha+\beta)^{-}\)	(c) \(\frac{2 a b}{a^2-b^2}\)
(IV) \(\tan (\alpha+\beta)=\)	(d) \(\frac{a^2-b^2}{a^2+b^2}\)
	(e) \(\frac{a^2+b^2}{a^2-b^2}\)

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Quadratic expression	The minimum value
(i) \(x^2-8 x+15\)	(a) \(\quad \frac{7}{2}\)
(ii) \(x^2-8 x+17\)	(b) \(\quad-1\)
(iii) \(2 x^2+4 x+7\)	(c) 1
iv) \(\left(x+\frac{5}{3}\right)^2+\frac{7}{2}\)	(d) 5