The pic posted by you ahows typical symptom of a disease called powdery mildew.
It is a fungal disease.
It is a common disease affecting many plants.
There are many ways to control this disease like chemical spraying and other organic ways. But, since you have mentioned that it is your kitchen garden and only one plant or few plants of brinjal are there,
Instead of spraying costly chemicals, i would suggest spraying of milk..! Yes..milk jn the quantity of 1 part milk to 10 parts water. Repeat Doses after 3 days depending on severiety
You can also spray neem oil or copper sulphate duted in water.
If this does not, control the disease, only then go for chemicals.
Hope that helps.