Find the values of p for which the power of a point ( 2,5 ) is negative w,r.t a circle
x^2 + y^2 - 8x - 12 y + p = 0 which neither touches the axes nor cuts them.
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Answer:
- given that x²+y²-8x-12y+p=0
- the center of the circle is (4,6)
- and radius r=√(16+36-p)=√(52-p)
- because this is not touching the axis nor cuts them so
- r<4 and r<6 ⇒ r<4
- by putting values
- √(52-p)<4
- squaring both side
- 52-p<16
- ⇒p>36
- now because the power is negative with respect to (2,5)
- 4+25-16-60+p<0
- p<47
- ⇒p∈(36,47)
- so the values of p is between 36 to 47.
Step-by-step explanation:
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