find the locus of the point p such that PA2+pb2=2c2 where A(a,0),B(-a,o) and 0<|a|<|c|​

Question

find the locus of the point p such that PA2+pb2=2c2 where A(a,0),B(-a,o) and 0<|a|<|c|​

in progress 0
Genesis 1 month 2021-08-19T02:33:18+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-19T02:35:04+00:00

    Q):-Find the equation of locus of a point P such that PA^2+PB^2=2C^2,Where A (a,0), B (-a,0) and o <11<|c|.

    Answer:-

    x^2+y^2+a^2-c^2=0.

    Explanation:-

    Let P (x,y) be a point on the locus

    given A (a,0),B (-a,0)

    given condition is PA^2+PB^2=2C^2

    (x-a)^2+(y-0)^2+(x+a)^2+(y-0)^2=2C^2

    x^2+a^2-2ax+y^2+x^2+a^2+2ax+y^2=2C^2

    2x^2+2y^2+2a^2-2C^2=0

    2 (x^2+y^2+a^2-c^2)=0

    x^2+y^2+a^2-C^2=0.

    Therefore Equation of locus of P is x^2+y^2+a^2-C^2=0.

    0
    2021-08-19T02:35:08+00:00

    \textbf{Given:}

    \text{P is the moving point and}

    PA^2+PB^2=2c^2

    \textbf{To find:}

    \text{The locus of P}

    \textbf{Solution:}

    \text{Let P(h,k) be the moving point}

    PA=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}

    PA=\sqrt{(h-a)^2+(k-0)^2}

    PA=\sqrt{(h-a)^2+k^2}

    PB=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}

    PB=\sqrt{(h+a)^2+(k-0)^2}

    PB=\sqrt{(h+a)^2+k^2}

    \text{Condition:}\;PA^2+PB^2=2c^2

    \implies\,(h-a)^2+k^2+(h+a)^2+k^2=2c^2

    \implies\,h^2+a^2-2ah+k^2+h^2+a^2+2ah+k^2=2c^2

    \implies\,h^2+a^2+k^2+h^2+a^2+k^2=2c^2

    \implies\,2h^2+2k^2+2a^2-2c^2=0

    \text{Divide by 2}

    \implies\,h^2+k^2+a^2-c^2=0

    \textbf{Answer:}

    \textbf{The locus of P is}

    \bf\,x^2+y^2+a^2-c2=0

    Find more:

    If A =(-2,3) and B=(4,1) are given points find the equation of locus of point P, such that PA=2PB.

    https://brainly.in/question/3201572

    B and c are fixed points having coordinates (3,0) and (-3,0) respectively. If the vertical angle bac is 90 then locus

    https://brainly.in/question/13799728

    Find the locus of the point x=a+b sec teta,y=b+a tan teta

    https://brainly.in/question/16779592

Leave an answer

Browse
Browse

18:9+8+9*3-7:3-1*13 = ? ( )