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`        No. Of the distinct normals that can be drawn to the ellipse x^2/169+y^2/25=1 from point p(0,6) is?`
3 years ago

```							equation of normal at point:(13cos∅,5sin∅) is13x/cos∅ - 5y/sin∅=144it passes through (0,6),therefore;(15+72sin∅=0) or (sin∅=-5/24)OR∅=2π-sin^-1(5/24) & π+sin^-1(5/24)hence,y axis is also one of the normals.
```
2 years ago
```							equation of normal at point can be written as ax/cos∅ - by/sin∅ = (ae)^2where e is eccentricity,a=13,b=5therefore equation of normal is13x/cos∅ - 5y/sin∅=144it passes through (0,6),therefore;(15+72sin∅=0) or (sin∅=-5/24)therefore there is 2 values of sin∅ which corresponds to 2 normals∅ = 2π - sin^-1(5/24) &∅ = π + sin^-1(5/24)also y axis is also one of the normals.therefore total 3 normals can be drawn
```
2 years ago
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