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harshit agarwal Grade: 12

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

8 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points

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

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8 years ago
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