(B) $1$. Find the midpoint $M$ of $AB$: $M = (\frac{4+2}{2}, \frac{3+5}{2}) = (3, 4)$.$2$. The distance of $P(x, y)$ from $M(3, 4)$ is at most $5$ uni

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$x^2+y^2-6x-8y \leq 0, x+y-7 < 0$

(B) $1$. Find the midpoint $M$ of $AB$: $M = (\frac{4+2}{2}, \frac{3+5}{2}) = (3, 4)$.$2$. The distance of $P(x, y)$ from $M(3, 4)$ is at most $5$ units: $(x-3)^2 + (y-4)^2 \leq 5^2$,which simplifies to $x^2 + y^2 - 6x - 8y \leq 0$.$3$. The equation of line $AB$ is $y - 3 = \frac{5-3}{2-4}(x - 4)$ $\Rightarrow y - 3 = -1(x - 4)$ $\Rightarrow x + y - 7 = 0$.$4$. The origin $(0, 0)$ satisfies $0 + 0 - 7 = -7 $5$. Combining these,the locus is $x^2 + y^2 - 6x - 8y \leq 0$ and $x + y - 7 < 0$.

Class 11 Mathematics 1 Conic Sections: Circle Locus Related Problem

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$A(4,3)$ and $B(2,5)$ are two points. If $P$ is a variable point on the same side as the origin with respect to the line $AB$ and is at most at a distance of $5$ units from the midpoint of $AB$,then the locus of $P$ is

AP EAMCET 2025 All AP EAMCET

A
$x^2+y^2-6x-8y=0$
B
$x^2+y^2-6x-8y \leq 0, x+y-7 < 0$
C
$x^2+y^2+6x+8y-25=0, x+y-7 \leq 0$
D
$x^2+y^2-6x+8y \geq 0, x+y-7 < 0$

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1 Conic Sections: Circle

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Locus Related Problem

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$A(4,3)$ and $B(2,5)$ are two points. If $P$ is a variable point on the same side as the origin with respect to the line $AB$ and is at most at a distance of $5$ units from the midpoint of $AB$,then the locus of $P$ is

Similar Questions

If $A(-a, 0)$ and $B(a, 0)$ are two fixed points,then the locus of the point $P(x, y)$ on which the line segment $AB$ subtends a right angle is:

Three distinct points $A, B$,and $C$ are given in a two-dimensional coordinate plane such that for each point,the ratio of its distance from $(1, 0)$ to its distance from $(-1, 0)$ is equal to $\frac{1}{3}$. What is the circumcenter of triangle $ABC$?

From the point $A(0, 3)$ on the circle $x^2 + 4x + (y - 3)^2 = 0$,a chord $AB$ is drawn and extended to a point $M$ such that $AM = 2 AB$. The equation of the locus of $M$ is:

The locus of the centroid of the triangle with vertices at $(a \cos \theta, a \sin \theta)$,$(b \sin \theta, -b \cos \theta)$ and $(1, 0)$ is (where $\theta$ is a parameter).

Two rods of lengths $a$ and $b$ slide along the coordinate axes in such a way that their ends are always concyclic. The locus of the center of the circle passing through the ends is:

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