STATEMENT-1: The locus of the centre of a circle which touches two given circles with different radius and centre will be a hyperbola.
and
STATEMENT-2: If the differnece of distance of a variable point to two given is always constant and less than the distnace between the points then the locus will be a hyperbola

Statement -1 is True, Statement-2 is True; Statement-2 is NOT a correct expalanation for Statement-1

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

Statement-1 is True, Statement-2 is False

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

Statement -1 is True, Statement-2 is True; Statement-2 is a correct expalanation for Statement-1

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

Statement-1 is False, Statement-2 is True.

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

Open in App

Solution

The correct option is C Statement -1 is True, Statement-2 is True; Statement-2 is a correct expalanation for Statement-1
Let $r_{1}, r_{2}$ be the radii of the given circles and $r$ be the radius of variable circle, Let $C - 1, C - 2, C$ be the centre of the given and the variable circles respectively, then
$C C_{1} = r + r_{1}$
$C C_{2} = r + r_{2}$
$\Rightarrow C C_{1} - C C_{2} = r_{1} - r_{2}$

Suggest Corrections

Similar questions

Describe:

(i) The locus of points at distances less than 3 cm from a given point.

(ii) The locus of points at distances greater than 4 cm from a given point.

(iii) The locus of points at distances less than 2.5 cm from a given point.

(iv) The locus of points at distances greater than or equal to 35 mm cm from a given point.

(v) The locus of the centre of a given circle which rolls around the outside of a second circle and is always touching it.

(vi) The locus of the centres of all circles that are tangent to both the arms of a given angle.

(vii) The locus of the mid-points of all chords parallel to a given chord of a circle.

(viii) The locus of points within a circle that are equidistant from the end points of a given chord.

- 1

B C

\frac{r_{2}}{r_{3}}

A

- 2

Join BYJU'S Learning Program