Guest

ax 2 +2bxy+ay 2 =c ; c>b>a>0. Minimum distance from origin is....

ax2+2bxy+ay2 =c ; c>b>a>0. Minimum distance from origin is....

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

Dear harshit

compair this with general equatin of second degree

it will be easly shown that this is hyperbola

since curve contain product of XY ,so its axix is not along the co ordinate axis,it is a rotated hyperbola.

since curve is symettric in x and y so it is rotated by 45 degree.

minimum distance can be calculated along the line perpendicular to the directrix. ie y=x

this line cut the parabola at ax2 +2bxx+ax2 =c

  or                                  x=+-(c/(2a+2b))1/2

so distance ={x2+x2}1/2

                  = <!-- /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0in; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman";} a:link, span.MsoHyperlink {color:blue; text-decoration:underline; text-underline:single;} a:visited, span.MsoHyperlinkFollowed {color:purple; text-decoration:underline; text-underline:single;} @page Section1 {size:8.5in 11.0in; margin:1.0in 1.25in 1.0in 1.25in; mso-header-margin:.5in; mso-footer-margin:.5in; mso-paper-source:0;} div.Section1 {page:Section1;} --> √2 x

                  = (c/(a+b))1/2


Please feel free to post as many doubts on our discussion forum as you can. If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly.
 We are all IITians and here to help you in your IIT JEE preparation.

 All the best.
 
Regards,
Askiitians Experts
Badiuddin

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free