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Find the equation of the normals to the circle `x^2+y^2-8x-2y+12=0` at the point whose ordinate is `-1`

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To find the equation of the normals to the circle \(x^2 + y^2 - 8x - 2y + 12 = 0\) at the point where the ordinate is \(-1\), we will follow these steps: ### Step 1: Rewrite the Circle's Equation First, we need to rewrite the equation of the circle in standard form. We can do this by completing the square. The given equation is: \[ x^2 + y^2 - 8x - 2y + 12 = 0 ...
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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
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  2. If the distances from the origin of the centers of three circles x^2+y...

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  3. Find the equation of the normals to the circle x^2+y^2-8x-2y+12=0 at t...

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  4. An infinite number of tangents can be drawn from (1,2) to the circle x...

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  5. If the circle x^2+y^2-4x-8y-5=0 intersects the line 3x-4y=m at two dis...

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  6. The line A x+B y+C=0 cuts the circle x^2+y^2+a x+b y+c=0 at Pa n dQ . ...

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  7. Find the equation of the circle which cuts the three circles x^2+y^2-3...

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  8. Find the equations to the common tangents of the circles x^2+y^2-2x-6y...

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  9. Equation of the smaller circle that touches the circle x^2+y^2=1 and p...

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  10. Show that the circles x^2+y^2-10 x+4y-20=0 and x^2+y^2+14 x-6y+22=0 to...

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  11. If the radical axis of the circles x^2+y^2+2gx+2fy+c=0 and 2x^2+2y^2+3...

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  12. The equation of three circles are given x^2+y^2=1,x^2+y^2-8x+15=0,x^2+...

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  13. If the circles x^2+y^2+2a^(prime)x+2b^(prime)y+c^(prime)=0 and 2x^2+2...

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  14. A circle passes through the origin and has its center on y=x If it cut...

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  15. Prove that the equation of any tangent to the circle x^2+y^2-2x+4y-4=0...

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  16. The tangent to the circle x^2+y^2=5 at (1,-2) also touches the circle ...

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  17. If S(1)=alpha^(2)+beta^(2)-a^(2), then angle between the tangents from...

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  18. If a >2b >0, then find the positive value of m for which y=m x-bsqrt(1...

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  19. Find the angle between the two tangents from the origin to the circle ...

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  20. Two circles C1 and C2 intersect at two distinct points PandQ in a line...

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