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

1

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2

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3

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0

(zero)

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Solution

The correct option is D $0$ (zero)
Number of intersecting points of the conic
Lets assume:
$C_{1} : 4 x^{2} + 9 y^{2} = 1$
$C_{2} : 4 x^{2} + y^{2} = 4$

They can be written as:
$C_{1} : \frac{x^{2}}{\frac{1}{4}} + \frac{y^{2}}{\frac{1}{9}} = 1$

$C_{2} : \frac{x^{2}}{1} + \frac{y^{2}}{4} = 1$

Plotting these on coordinate axes, we get the following figure.
We can see that there is no intersection.
Hence, zero point of intersections.

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Similar questions

Q. Number of intersecting points of the conics

4 x^{2} + 9 y^{2} = 1

and

4 x^{2} + y^{2} = 4

Q. Number of intersecting points of the conic

4 x^{2} + 9 y^{2} = 1

and

4 x^{2} + y^{2} = 4

Q. The ellipse

4 x^{2} + 9 y^{2} = 36

and the hyperbola

4 x^{2} - y^{2} = 4

have the same food and they intersect at right angles then the equation of the circle through the points of intersection of two conics is

Q. If the ellipse

4 x^{2} + 9 y^{2} = 36

and the hyperbola

a^{2} x^{2} - y^{2} = 4

intersect at right angles, then which among the following options are correct

If C is the center and A,B are two points on the conic ${4 x}^{2}$ + ${9 y}^{2}$ -8 $x$ -36y +4=0
$∠$ ACB = $\frac{π}{2}$ , then ${C A}^{- 2}$ + ${C B}^{- 2}$ + $\frac{23}{36}$ =

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Number of intersecting points of the conic 4x2+9y2=1 and 4x2+y2=4 is

The correct option is D 0 (zero)Number of intersecting points of the conic Lets assume:C1:4x2+9y2=1C2:4x2+y2=4They can be written as:C1:x214+y219=1C2:x21+y24=1Plotting these on coordinate axes, we get the following figure.We can see that there is no intersection.Hence, zero point of intersections.

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