SATHEE: Circle 5 Question 7

Circle 5 Question 7

7. The equations of the tangents drawn from the origin to the circle $x^{2} + y^{2} + 2 r x + 2 h y + h^{2} = 0$ , are

$(1988, 2 M)$

(a) $x = 0$

(b) $y = 0$

(d) $(h^{2} - r^{2}) x + 2 r h y = 0$

Assertion and Reason

For the following questions, choose the correct answer from the codes (a), (b), (c) and (d) defined as follows.

(a) Statement I is true, Statement II is also true;

Statement II is the correct explanation of Statement I.

(b) Statement I is true, Statement II is also true; Statement II is not the correct explanation of Statement I

(d) Statement I is false; Statement II is true

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Answer:

Correct Answer: 7. $(a, c)$

Solution:

Since, tangents are drawn from origin. So, the equation of tangent be $y = m x$ .

$\Rightarrow$ Length of perpendicular from origin $=$ radius

$\begin{aligned} \Rightarrow & \frac{| m r + h |}{\sqrt{m^{2} + 1}} & = r \\ \Rightarrow & m^{2} r^{2} + h^{2} + 2 m r h & = r^{2} (m^{2} + 1) \\ \Rightarrow & m & = \frac{r^{2} - h^{2}}{2 r h}, m = \infty \end{aligned}$

$∴$ Equation of tangents are $y = \frac{r^{2} - h^{2}}{2 r h} x, x = 0$

Therefore (a) and (c) are the correct answers.

Circle 5 Question 7

7. The equations of the tangents drawn from the origin to the circle $x^{2} + y^{2} + 2 r x + 2 h y + h^{2} = 0$ , are

Assertion and Reason

Answer:

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Circle 5 Question 7

7. The equations of the tangents drawn from the origin to the circle x2+y2+2rx+2hy+h2=0, are

Assertion and Reason

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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7. The equations of the tangents drawn from the origin to the circle $x^{2} + y^{2} + 2 r x + 2 h y + h^{2} = 0$ , are