Does the point (-2.5, 3.5) lie inside, outside or on the circle x… - Vidyadip

Question

Does the point $(-2.5, 3.5)$ lie inside, outside or on the circle $x^2 + y^2 = 25$?

✓

Answer

The equation of the given circle is $x^2 + y^2 = 25. x^2 + y^2 = 25 $
$\Rightarrow (x - 0)^2 + (y - 0)^2 = 5^2$, which is of the form $(x - h)^2 + (y - k)^2 = r^2$, where h = 0, k = 0, and r = 5.
$\therefore$ Centre = (0, 0) and radius = 5 Distance between point (-2.5, 3.5) and centre (0, 0) $=\sqrt{(-2.5-0)^2+(3.5-0)^2}$ $=\sqrt{6.25+12.25}$ $=\sqrt{18.5}$
$=4.3(\text{approx.})<5$ Since the distance between point (-2.5, 3.5) and centre (0, 0) of the circle is less than the radius of the circle, point (-2.5, 3.5) lies inside the circle.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 4 marks)" from CONIC SECTIONS→CONIC SECTIONS — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Solve the following equations: $\sqrt{3}\cos\text{x}+\sin\text{x}=1$

Using properties of sets, show that for any two sets A and $\text{B},\text{ (A}\cup\text{B})\cap(\text{A}\cup\text{B}')=\text{A}.$

Prove that: $\frac{\sin\text{A}\sin2\text{A}+\sin3\text{A}\sin6\text{A}}{\sin\text{A}\cos2\text{A}+\sin3\text{A}\cos6\text{A}}=\tan5\text{A}$

If (a - b), (b - c), (c - a) are in G.P., then prove that: $\big(\text{a}+\text{b}+\text{c}\big)^2=3\big(\text{ab}+\text{bc}+\text{ca}\big)$

Evaluate the following: $\sum\limits^5_\text{r=1}\ ^5\text{C}_{\text{r}}$

If for $\text{f}(\text{x})=\lambda\text{x}^2+\mu\text{x}+12,\text{f}'(\text{x})=15$ and $\text{f}'(\text{2})=11,$ then find $\lambda$and $\mu.$

In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

Express the following complex numbers in the form $\text{r}(\cos\theta+\text{i}\sin\theta):$ $\frac{1-\text{i}}{\cos\frac{\pi}{3}+\text{i}\sin\frac{\pi}{3}}$

Determine the points yz-plane equidistant from the points $A(1, -1, 0), B(2, 1, 2)$ and $C(3, 2, -1)$.

For any two sets A and B, prove the following: $\text{A}-\text{(A}-\text{B})=\text{A}\cap\text{B}$