AP EAMCET · Maths · Circle

If $y=\sqrt{3} x+k_1$ and $y=\sqrt{3} x+k_2$ are two parallel tangents of a circle of radius 2 units, then $\left|k_1-k_2\right|$ is equal to

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Correct Answer

(B) 8

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Detailed explanation

The distance between parallel tangents to a circle is equals to the diameter of the circle, so $\begin{aligned} & \frac{\left|k_1-k_2\right|}{\sqrt{1+3}}=4 \\ \Rightarrow \quad & \left|k_1-k_2\right|=8 \end{aligned}$ Hence, option (b) is correct.

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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The standard deviations of $x_{i} (i = 1, 2, \dots . 10)$ and $y_{i} (i = 1, \dots 10)$ are respectively $a$ and $b$ . $\bar{x}, \bar{y}$ are the means of these two sets of observations respectively. If $z_{i} = (x_{i} - \bar{x}) (y_{i} - \bar{y})$ and $\sum_{i = 1}^{10} z_{i} = c$ , then the standard deviation of the observations $(x_{i} - y_{i}), (i = 1, 2, \dots 10)$ is

AP EAMCET 2019 Medium

A body is projected horizontally from the top of a tower of height

180 m

with a velocity of

20 {ms}^{- 1}

. If acceleration due to gravity is

10 {ms}^{- 2}

then match the following.

List-I		List-II
$(A)$	Velocity of the body after $1$ second $($ in ${ms}^{- 1}$ )	(I)	$5$
$(B)$	Horizontal displacement of the body after $1$ second (in meters)	(ii)	$20$
$(C)$	Vertical displacement of the body after $1$ second (in meters)	(iii)	$10$
$(D)$	Vertical velocity of the body after $1$ second $($ in ${ms}^{- 1}$ )	(iv)	$22.4$

The correct answer is

AP EAMCET 2018 Medium

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If \(y=\sqrt{3} x+k_1\) and \(y=\sqrt{3} x+k_2\) are two parallel tangents of a circle of radius 2 units, then \(\left|k_1-k_2\right|\) is equal to

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Step-by-step Solution

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