MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Direction Cosines

xy=a2 and x...

Question

$x y = a^{2}$ and $x^{2} + y^{2} = 2 a^{2}$
These two curves :

A

touch.

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B

intersect

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

never intersect

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

none of the above

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A touch.
Touch: The two curves meet where $(x^{2} - a^{2}) = 0$
$∴ x = a, - a$ and so $y = \frac{a^{2}}{x} = a$ or $- a .$
Hence the points are $(a, a)$ or $(- a, - a) .$
$\frac{d y}{d x^{1}} = - \frac{y}{x} = - 1. {\frac{d y}{d x}}_{I I} = - \frac{x}{y} = - 1$
Hence the curves touch.

Suggest Corrections

thumbs-up

0

Similar questions

x y = a^{2}

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

touch each other.

Q. The angle of intersection of the curves

x y = a^{2}

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

Q. Find the angle of intersection of the curves

x y = a^{2}

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

Q. The angle of intersection of the curves xy = a² and x² − y² = 2a²is

(a) 0°
(b) 45°
(c) 90°
(d) none of these

Q. The angle between the curves

x^{2} + y^{2} = \sqrt{2} a^{2}

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

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Direction Cosines and Direction Ratios

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Direction Cosines

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon