If A = {(x, y) : x^2 + y^2 = 25} and B = {(x, | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given sets are $A = \{(x, y) : x^2 + y^2 = 5^2\}$ which represents a circle with center $(0, 0)$ and radius $r = 5$.$B = \{(x, y) : x^2 + 9y^2 = 1

Vedclass · Accepted Answer

Four points

Vedclass · Answer

(D) Given sets are $A = \{(x, y) : x^2 + y^2 = 5^2\}$ which represents a circle with center $(0, 0)$ and radius $r = 5$.$B = \{(x, y) : x^2 + 9y^2 = 144\}$. Dividing by $144$,we get $\frac{x^2}{144} + \frac{9y^2}{144} = 1$,which simplifies to $\frac{x^2}{12^2} + \frac{y^2}{4^2} = 1$. This represents an ellipse with semi-major axis $a = 12$ and semi-minor axis $b = 4$.Since the circle has radius $5$ and the ellipse has semi-minor axis $4$ and semi-major axis $12$,the circle intersects the ellipse at four distinct points because the radius of the circle is greater than the semi-minor axis but less than the semi-major axis of the ellipse.Thus,$A \cap B$ contains four points.

If $A = \{(x, y) : x^2 + y^2 = 25\}$ and $B = \{(x, y) : x^2 + 9y^2 = 144\}$,then $A \cap B$ contains

Similar Questions

The locus of the midpoints of the chords of the hyperbola $x^2 - y^2 = a^2$ which touch the parabola $y^2 = 4ax$ is:

The slope of a common tangent to the ellipse $\frac{x^2}{49}+\frac{y^2}{4}=1$ and the circle $x^2+y^2=16$ is

If the common tangents to the parabola $x^2 = 4y$ and the circle $x^2 + y^2 = 4$ intersect at the point $P$,then find the square of the slope of the line.

Number of intersecting points of the conics $4x^{2} + 9y^{2} = 1$ and $4x^{2} + y^{2} = 4$ is

Let $P$ be the point of intersection of the common tangents to the parabola $y^2 = 12x$ and the hyperbola $8x^2 - y^2 = 8$. If $S$ and $S'$ denote the foci of the hyperbola where $S$ lies on the positive $x$-axis,then $P$ divides $SS'$ in the ratio:

Vedclass Test Series

Exam Paper Generator

Online Exam Module