If with standard notations $t_{1}, t_{2}, t_{3}, t_{4}$ are four co–normal points on the hyperbola $x y = c^{2}$ then the orthocentre of the triangle formed by joining the points $t_{1}, t_{2}, t_{3}$ is given by

(0, 0)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(c t_{4}, \frac{c}{t_{4}})

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

[c (t_{1} + t_{2} + t_{3}), \frac{c}{t_{1} + t_{2} + t_{3}}]

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(\frac{c}{t_{4}}, c t_{4})

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $(c t_{4}, \frac{c}{t_{4}})$
For a triangle formed by joining any three co-normal points, orthocenter coincides with the fourth point.

Suggest Corrections

Similar questions

Q. Assertion :If points

A (c t_{1}, \frac{c}{t_{1}})

B (c t_{2}, \frac{c}{t_{2}})

C (c t_{3}, \frac{c}{t_{3}})

and

D (c t_{4}, \frac{c}{t_{4}})

lies on the circle

x^{2} + y^{2} + 2 g x + 2 f y + k = 0

then

t_{1} + t_{2} + t_{3} + t_{4} = - \frac{2 g}{c}

. Reason: Points

A, B, C, D

are parametric points of

x y = c^{2}

If a circle and the rectangular hyperbola $x y = c^{2}$ meet in the four points $t_{1} . t_{2} . t_{3} & t_{4}$ then $t_{1} . t_{2} . t_{3} t_{4}$ is equal to______

If a circle cuts a rectangular hyperbola $x y = c^{2}$ in A,B,C,D and the parameters of these four points be $t_{1}, t_{2}, t_{3}$ and $t_{4}$ respectively. Then if the eccentricity of a conic is equal to $t_{1} . t_{2} . t_{3} . t_{4}$ , the conic can't be

If a circle and rectangular hyperbola $x y = c^{2}$ meet in the four points $t_{1}, t_{2}, t_{3} & t_{4}$ . Then which of the following statements are correct?
1. The center of the mean position of the four points bisects the distance between the center of the two curve.
2. Center of the circle through the points $t_{1}, t_{2} & t_{3}$ is: $[(\frac{c}{2} (t_{1} + t_{2} + t_{3}) + \frac{1}{t_{1} . t_{2} . t_{3}}), \frac{c}{2} (\frac{1}{t_{1}} + \frac{1}{t_{2}} + \frac{1}{t_{3}} + t_{1} t_{2} t_{3})]$

Let $θ \in (0, \frac{π}{4}) a n d t_{1} = (t a n θ)^{t a n θ}, t_{2} (t a n θ)^{c o t} t_{3} = (c o t θ)^{t a n θ} a n d t_{4} (c o t θ)^{t a n θ}$ , then

Join BYJU'S Learning Program

If with standard notations t1,t2,t3,t4 are four co–normal points on the hyperbola xy=c2 then the orthocentre of the triangle formed by joining the points t1,t2,t3 is given by

The correct option is B (ct4,ct4)For a triangle formed by joining any three co-normal points, orthocenter coincides with the fourth point.

If with standard notations $t_{1}, t_{2}, t_{3}, t_{4}$ are four co–normal points on the hyperbola $x y = c^{2}$ then the orthocentre of the triangle formed by joining the points $t_{1}, t_{2}, t_{3}$ is given by

The correct option is B $(c t_{4}, \frac{c}{t_{4}})$
For a triangle formed by joining any three co-normal points, orthocenter coincides with the fourth point.