Which of the following statements are true and which are false? In each case give a valid reason for saying so
$r :$ Circle is a particular case of an ellipse.

True

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False

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Solution

The correct option is A True
Relation in ellipse and circle:
The ellipse is a type of circle. Consider the ellipse equation $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ .
If $a = b = 1$ , $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ become $x^{2} + y^{2} = 1$ . which is a circle equation. As a result, the circle represents a unique type of ellipse.
Hence, the statement $r$ is True.

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\sqrt{11}

Which of the following statements are true and which are false ? In each case give a valid reason for saying so

(i) p : Each radius of a circle chord of the circle.

(ii) q : The centre of a circle bisects each chord of the circle.

(iii) r : Circle is a particular case of am ellipse.

(iv) s If x and y are integers such that x > y, then -x < -y .

(v) $t : \sqrt{11}$ is a rational number.

Which of the following statements are true and which are false? In each case give a valid reason for saying so.

(i) p: Each radius of a circle is a chord of the circle.

(ii) q: The centre of a circle bisects each chord of the circle.

(iii) r: Circle is a particular case of an ellipse.

(iv) s: If x and y are integers such that x > y, then –x < –y.

(v) t: is a rational number.

x > y

- x < - y

\sqrt{11}

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