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Show that the line lx+my+n=0 is a normal...

Show that the line `lx+my+n=0` is a normal to the circles S=0 iff `gl+mf=mn`.

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Show that the line lx+my + n =0 is a normal to the circle S = 0 if and only if gl +mf = n

If S-=x^(2)+y^(2)+2gx=2fy+c=0 represents a circle then show that the straight line lx+my=n=0 (i) touches the circle S=0 if g^(2)+f^(2)-c=(gl+mf-n)^(2)/(l^(2)+m^(2)) (ii) meets the circle S=0 in two points if g^(2)+f^(2)-cgt((gl+mf-n)^(2))/(l^(2)+m^(2)) (iii) will not meet the circle if g^(2)+f^(2)-clt((gl+mf-n)^(2))/(l^(2)+m^(2))

Find the condition for the line Ix+my+ n = 0 is a normal to the circle x^2 + y^2 + 2gx + 2fy + c = 0 .

The condition that the line lx + my + n= 0 to be a normal to the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2))= 1 is

The condition that the line lx +my+n =0 to be a normal to y^(2)=4ax is

A : The condition that the line x/p+y/q=1 to be a tangent to the parabola y^(2)=4ax is ap+ q^(2) =0. R: The condition that the line lx+my+n=0 may touch the parabola y^(2)=4ax is am^(2) = In

If the line ax + by + c = 0 is a normal to the curve xy = K^(2) then show that a and b have opposite signs.

AAKASH SERIES-CIRCLES-PRACTICE EXERCISE
  1. Show that the line lx+my+n=0 is a normal to the circles S=0 iff gl+mf=...

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  2. The circle with centre (1,1) and radius 1 is

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  3. For a circle two diameter are x+y=3, x-y=1 then centre is

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  4. Circle with centre (-1,2) and passing through origin is

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  5. The equation of the circle concentric with x^(2)+y^(2)-6x+4y-3=0 and h...

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  6. The equation of the circle concentric with x^(2)+y^(2)-2x+8y-23=0 and ...

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  7. For the circle x^(2)+y^(2)-4x+2y+c=0 radius is 4 then c=

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  8. If A(1),A(2),A(3) be the areas of circles x^(2)+y^(2)+4x+6y-19=0, x^(2...

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  9. The equation of the circle with centre (2,3) and distance between (0,0...

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  10. The equation of the circle with radius 4 and centres as the midpoint o...

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  11. The circle with centre (1,-3) and radius being the distance between th...

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  12. If the area of the circle x^(2)+y^(2)+4x+2y+k=0 is 5pi square cms then...

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  13. If (2,3) is an extremity of a diameter of the circle x^(2)+y^(2)-5x-8y...

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  14. The line x/a+y/b=1 meets the axis of and y at A and B respectively and...

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  15. Equation of circle with centre (-1,2) and passing through the centroid...

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  16. The centroid of an equilateral triangle is (0, 0) and the length of th...

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  17. Equation of the circle with radius 10 and whose two diameters are x+y=...

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  18. If a circle is inscribed in a square of side 10, so that the circle t...

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  19. Show that the equation of the circle which pass through the points (1,...

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  20. If the abscissae of points A, B are the roots of the equation x^(2) + ...

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  21. The abscissae of two points A and B are the roots of the equation x^(2...

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