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

Byju's Answer

Standard XII

Mathematics

Slope of a Line

Assertion ( ...

Question

Assertion ( $A$ ) The equation to the locus of points which are equidistant from the points $(- 3, 2)$ , $(0, 4)$ is $6 x + 4 y - 3 = 0$
Reason ( $R$ ) The locus of points which are equidistant to $A, B$ is perpendicular bisector of $A B$

A

true,

R

true and

R

is correct explanation of

A

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

A

true,

R

true but

R

is not correct explanation

A

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

A

true,

R

false

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

A

false,

R

true

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

Open in App

Solution

The correct option is A $A$ true, $R$ true and $R$ is correct explanation of $A$ .
Let $(h, k)$ be the points which are equidistant from point $(- 3, 2)$ and $(0, 4)$
Then equation of the locus of points is given by
$(h + 3)^{2} + (k - 2)^{2} = (h - 0)^{2} + (k - 4)^{2}$
$⟹ h^{2} + 6 h + 9 + k^{2} - 4 k + 4 = h^{2} + k^{2} - 8 k + 16$
$⟹ 6 h + 4 k - 3 = 0$
$∴ 6 x + 4 y - 3 = 0$
This is the perpendicular bisector of the line joining $(- 3, 2)$ and $(0, 4)$
Hence, both $A$ and $R$ are true and $R$ is correct explanation of $A$ .

Suggest Corrections

Similar questions

Q. Assertion (A)
The system of equations

3 x - 2 y + 1 = 0 and 6 x - 4 y + 3 = 0

is inconsistent.
Reason (R)
The system of equations

a_{1} x + b_{1} y + c_{1} = 0 and a_{2} x + b_{2} y + c_{2} = 0

has a unique solution when

\frac{a_{1}}{b_{2}} \neq \frac{b_{1}}{b_{2}} .

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

$Assertion - --------- -$ (A): The boiling point of HF is higher than that of $H_{2} O$ .
$Reason - ------ -$ (R): The hydrogen bond strength in HF is lower than that in $H_{2} O$ .

Q. Assertion (A)
The equation

2 x^{2} - 4 x + 3 = 0

has no real roots.

Reason (R)
The equation

a x^{2} + b x + c = 0, (a \neq 0)

has no real roots, if

(b^{2} - 4 a c) < 0 .

Q. Assertion (A)
If two tangents are drawn to a circle from an external point, they subtend equal angles at the centre.

Reason (R)
A parallelogram circumscribing a circle is a rhombus.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R)is true.

Q. Assertion(A): Some algae are unicellular.
Reason(R): They belong to the kingdom Monera.

Join BYJU'S Learning Program

Assertion (A) The equation to the locus of points which are equidistant from the points(−3,2), (0,4) is 6x+4y−3=0Reason (R) The locus of points which are equidistant to A,B is perpendicular bisector of AB

Assertion ( $A$ ) The equation to the locus of points which are equidistant from the points $(- 3, 2)$ , $(0, 4)$ is $6 x + 4 y - 3 = 0$
Reason ( $R$ ) The locus of points which are equidistant to $A, B$ is perpendicular bisector of $A B$