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If the straight line lx+my+n=0 touches t...

If the straight line `lx+my+n=0` touches the :
hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`, show that `a^(2) l^(2)-b^(2)m^(2)=n^(2)`.

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If the straight line lx+my=n is a normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 show that (a^(2))/(l^(2))-(b^(2))/(m^(2))=((a^(2)+b^(2))^(2))/(n^(2)) .

If the line lx+my=1 is normal to the hyperbola (x^(2))/(9)-(y^(2))/(4)=1 , show that (9)/(l^(2))-(4)/(m^(2))=169

Find the condition that the straight line lx+my=n touches the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

If the straight line lx+my+n=0 touches the : parabola y^(2)=4ax , prove that am^(2)=nl

If the straight line lx+my+n=0 touches the : circle x^(2)+y^(2)=a^(2) , show that a^(2)(l^(2)+m^(2))=n^(2)

The line y= mx +c touches the hyperbola b^(2) x^(2) - a^(2) y^(2) = a^(2)b^(2) if-

If the straight line lx+my+n=0 touches the : circle x^(2)+y^(2)+2agx+2fy+c=0 show that, (l^(2)+m^(2))(g^(2)+f^(2)-c)= (gl+ fm-n)^(2)

If the straight line xcosalpha+ysinalpha=p touches the curve (x^2)/(a^2)+(y^2)/(b^2)=1 , then prove that a^2cos^2alpha-b^2sin^2alpha=p^2 .

Show that the locus of the midpoints of the chords of the circle x^(2)+y^(2)=a^(2) which are tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is (x^(2)+y^(2))^(2)=a^(2)x^(2)-b^(2)y^(2) .

The slope of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( x_(1),y_(1)) is-

CHHAYA PUBLICATION-TANGENT AND NORMAL -LONG ANSWER TYPE QUESTIONS
  1. If the straight line lx+my+n=0 touches the : parabola y^(2)=4ax, pr...

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  2. Find the condition that the straight line lx+my=n touches the ellipse ...

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  3. If the straight line lx+my+n=0 touches the : hyperbola (x^(2))/(a^(2...

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  4. If the straight line y= x sin alpha+ a sec alpha be a tangent ot the c...

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  5. Find the condition that the straight line x cos theta+ y sin theta =p ...

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  6. Find the condition that the straight line x cos alpha+ y sin alpha=p i...

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  7. hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1.

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  8. If the straight line lx+my=1 touches th curve (ax)^(n)+(by)^(n)=1. The...

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  9. If the straigjht line x cos alpha+ y sin alpha=p touches the curve x^(...

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  10. Show that the tangents at the ends of latus rectum of an ellipse inter...

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  11. Find the equation of the common tangent to the circle x^(2)+y^(2)=8 an...

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  12. Find the equation o of the common tangent to the parabolas y^(2)=32x ...

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  13. Find the common tangents to the hyperbola x^(2)-2y^(2)=4 and the circl...

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  14. The equation of the tangent to the curve y^(2)=ax^(3)+b at the point (...

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  15. In each of the following cases find the angle between the given curves...

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  16. In each of the following cases find the angle between the given curves...

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  17. Show that curves x^(3)-3xy^(2)+2=0 and y^(3)-3x^(2)y+2=0 intersect at ...

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  18. If the curves ax^(2)+by^(2)=1 and cx^(2)+dy^(2)=1 intersect at right a...

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  19. The equation of the tangent to the curve y=a+bx+cx^() where it meet th...

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  20. If x(1) and y(1) be the intercepts on the x and y-axis respectively of...

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