The rectangular hyperbola xy=42 does not intersect the parabola y2=4x in real point.tatement-2: If hyperbola x2b2−y2a2=1 passes through the focus of ellipse x2a2+y2b2=1 then eccentricity of the hyperbola is 3.

Statement-1 is false as the point (4, 4) lies on both the curves. In statmetn-2 if e is the eccentricity of the ellipse, thena2e2b2=1⇒e2=b2a2⇒a2−b2a2=b2a2⇒a2=2b2eccentricity of the hyperbola is b2+a2b2=3the statement-2 is true.

The rectangular hyperbola xy=42 does not intersect the parabola y2=4x in real point.tatement-2: If hyperbola x2b2−y2a2=1 passes through the focus of ellipse x2a2+y2b2=1 then eccentricity of the hyperbola is 3.

Statement-1 is false as the point (4, 4) lies on both the curves. In statmetn-2 if e is the eccentricity of the ellipse, thena2e2b2=1⇒e2=b2a2⇒a2−b2a2=b2a2⇒a2=2b2eccentricity of the hyperbola is b2+a2b2=3the statement-2 is true.

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

The rectangular hyperbola $x y = 4^{2}$ does not intersect the parabola $y^{2} = 4 x$ in real point.
tatement-2: If hyperbola $\frac{x^{2}}{b^{2}} - \frac{y^{2}}{a^{2}} = 1$ passes through the focus of ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ then eccentricity of the hyperbola is $\sqrt{3}$ .

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

STATEMENT-1 is True, STATEMENT-2 is True;
STATEMENT-2 is a correct explanation for STATEMENT-1

STATEMENT-1 is False, STATEMENT-2 is True

STATEMENT-1 is True, STATEMENT-2 is True;
STATEMENT-2 is NOT a correct explanation for STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is False

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Statement-1 is false as the point (4, 4) lies on both the curves.

In statmetn-2 if $e$ is the eccentricity of the ellipse, then

$\frac{a^{2} e^{2}}{b^{2}} = 1 \Rightarrow e^{2} = \frac{b^{2}}{a^{2}} \Rightarrow \frac{a^{2} - b^{2}}{a^{2}} = \frac{b^{2}}{a^{2}} \Rightarrow a^{2} = 2 b^{2}$