Co-Normal Points

Statement :1 If a parabola y ^(2) = 4ax intersects a circle in three co-normal points then the circle also passes through the vertr of the parabola. Because Statement : 2 If the parabola intersects circle in four points t _(1), t_(2), t_(3) and t_(4) then t _(1) + t_(2) + t_(3) +t_(4) =0 and for co-normal points t _(1), t_(2) , t_(3) we have t_(1)+t_(2) +t_(3)=0.

From the point (15,12), three normals are drawn to the parabola y^(2)=4x. Then centroid and triangle formed by three co-normals points is (A)((16)/(3),0) (B) (4,0) (C) ((26)/(3),0) (D) (6,0)

STATEMENT-1 :The locus of centroid of a triangle formed by three co-normal points on a parabola is the axis of parabola. STATEMENT-2 : One of the angles between the parabolas y^(2) =8x and x^(2) = 27y is tan^(-1)((9)/(13)). STATEMENT-3 : Consider the ellipse (x^(2))/(9) + (y^(2))/(4) =1 THe product of lengths of perpendiculars drawn from foci to a tangent is 4.

Point OF tangency , Properties OF normal, Conormal points,Chord OF contact , Illustration

In parabola y^2=4x, From the point (15,12), three normals are drawn to the three co-normals point is

Pair OF Tangent|| Chord OF Contact|| Length OF Subtangent and Sub Normal|| Point OF Intercept OF Tangent|| Important Point OF Normal

Equation of normal in Point form

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