Find the equation of the tangent to the circle x² + y² = 9, which passes through the point on the circle where x = 2 and y is positive.

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RRB NTPC Exam 19 Jan 2021 click here to view all questions

Find the equation of the tangent to the circle x² + y² = 9, which passes through the point on the circle where x = 2 and y is positive.

A√5y = 2x – 9

B√5y = –2x + 9

C2y = –√5x + 4√5

D2y = –√5x – 4√5

Akhilesh ? Apr 18 '25 at 11:28

correct answer is: option b : √5y = –2x + 9
Explanation:

\(x^2 + y^2 = 9\)

Given the circle equation \(x^2 + y^2 = 9\), we need to find the equation of the tangent at the point where \(x = 2\) and \(y\) is positive.

Step 1: Find the point of tangency

Substitute \(x = 2\) into the circle equation to find \(y\):

\(2^2 + y^2 = 9 \implies 4 + y^2 = 9 \implies y^2 = 5 \implies y = \sqrt{5}\) (since \(y\) is positive)

Thus, the point of tangency is \((2, \sqrt{5})\)

Step 2: Use the tangent line formula

The equation of the tangent to the circle at point \((x_1, y_1)\) is given by:

\(xx_1 + yy_1 = r^2\)

Substituting \((x_1, y_1) = (2, \sqrt{5})\) and \(r = 3\):

\(2x + \sqrt{5}y = 9\)

Step 3: Match with the given options

Rearrange the equation to match the options:

\(\sqrt{5}y = -2x + 9\)

This corresponds to option b: \(\sqrt{5}y = -2x + 9\)

Final Answer: \(\boxed{\sqrt{5}y = -2x + 9}\)

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If tan A + cot A = 4, find the value of tan^2A + cot^2A

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KPTCL Assistant Exam (Mescom) SLOT-3 2017 click here to view all questions

If tan A + cot A = 4, find the value of tan^2A + cot^2A

A14

B20

C35

D40

No answer description available for this question. Let us discuss.

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A fair coin is tossed 3 times in succession. If the first to

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PGCET CSE Exam (Karnataka) 2011 click here to view all questions

A fair coin is tossed 3 times in succession. If the first toss produced a head, then the probability of getting exactly two heads in 3 tosses ( including the first toss ) is

A1/8

B3/8

C1/2

D3/4

Akilesh Kharvi ? Dec 8 '2016 at 21:11

Answer:\(\frac{3}{4}\)

Explanation:

P(2 heads in 3 tosses / first toss is a head) 
(H,H,H) 
(H,H,T) 
(H,T,H) 
(H,T,T) 
(T,H,H) 
(T,H,T) 
(T,T,H) 
(T,T,T) 
are the 2^3 = 8 ways in which the coin can roll. 
Since we are given that the first toss is a head, our sample space becomes: 
(H,H,H) 
(H,H,T) 
(H,T,H) 
(H,T,T) 
Of these four possibilities, we want to know how many have exactly 2 heads 
\(= \frac{3}{4}\)

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The probability of two sisters sharing the same birth-month

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PGCET CSE Exam (Karnataka) 2011 click here to view all questions

The probability of two sisters sharing the same birth-month is

A1/144

B1/24

C1/12

D1/6

Akilesh Kharvi ? Dec 8 '2016 at 21:6

Answer: \(\frac{1}{12}\)

Explanation:

The first sister can be born any month, it makes no difference.
The second sister has 1/12 chance of being born in the same month.

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A U B and A B are equal only if

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PGCET CSE Exam (Karnataka) 2011 click here to view all questions

A U B and A B are equal only if

AA is an empty set

BB is an empty set

Cboth A and B are empty sets

Dboth A and B are singleton sets

Akilesh Kharvi ? Dec 8 '2016 at 21:8

Answer: both A and B are empty sets 

Explanation:

Let B = A + X 
A U B = { A, X } 
A ∩ B = { A } 
Thus A U B = A ∩ B only if X is the empty set. 
In that case, A = B

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